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Jika , maka nilai dari , untuk  adalah ....

Pertanyaan

Jika f open parentheses x close parentheses equals negative 4 plus x, maka nilai dari f open parentheses x squared close parentheses minus open parentheses f open parentheses x close parentheses close parentheses squared plus 3 f open parentheses x close parentheses, untuk x equals negative 2 adalah ....

  1. 18 

  2. 6 

  3. negative 18  

  4. negative 36 

  5. negative 54 

Pembahasan Soal:

Gunakan konsep nilai fungsi.

Diketahui:
f open parentheses x close parentheses equals negative 4 plus x, akan ditentukan nilai dari f open parentheses x squared close parentheses minus open parentheses f open parentheses x close parentheses close parentheses squared plus 3 f open parentheses x close parentheses, untuk x equals negative 2.

Perhatikan perhitungan berikut.

f open parentheses x close parentheses equals negative 4 plus x table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x squared close parentheses minus open parentheses f open parentheses x close parentheses close parentheses squared plus 3 f open parentheses x close parentheses end cell equals cell f open parentheses open parentheses negative 2 close parentheses squared close parentheses minus open parentheses f open parentheses negative 2 close parentheses close parentheses squared plus 3 f open parentheses negative 2 close parentheses end cell row blank equals cell f open parentheses 4 close parentheses minus open parentheses f open parentheses negative 2 close parentheses close parentheses squared plus 3 f open parentheses negative 2 close parentheses end cell row blank equals cell open parentheses negative 4 plus 4 close parentheses minus open parentheses negative 4 minus 2 close parentheses squared plus 3 open parentheses negative 4 minus 2 close parentheses end cell row blank equals cell 0 minus open parentheses negative 6 close parentheses squared plus 3 open parentheses negative 6 close parentheses end cell row blank equals cell negative 36 minus 18 end cell row blank equals cell negative 54 end cell end table 

Diperoleh nilai dari f open parentheses x squared close parentheses minus open parentheses f open parentheses x close parentheses close parentheses squared plus 3 f open parentheses x close parentheses, untuk x equals negative 2 adalah negative 54.

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Dwi

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

Jika  dan , maka tentukan nilai .

Pembahasan Soal:

Dengan menggunakan cara mencari nilai fungsi dan perkalian dua fungsi diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses x close parentheses times g open parentheses x close parentheses end cell row cell open parentheses f times g close parentheses open parentheses 2 close parentheses end cell equals cell f open parentheses 2 close parentheses times g open parentheses 2 close parentheses end cell row blank equals cell open parentheses 2 open parentheses 2 plus 3 close parentheses close parentheses times open parentheses 2 squared minus 1 close parentheses end cell row blank equals cell open parentheses 2 times 5 close parentheses open parentheses 4 minus 1 close parentheses end cell row blank equals cell 10 times 3 end cell row blank equals 30 end table end style

Dengan demikian hasil dari begin mathsize 14px style open parentheses f times g close parentheses open parentheses 2 close parentheses end style adalah begin mathsize 14px style 30 end style.

0

Roboguru

Diberikan  dan . Jika , maka nilai dari  adalah ....

Pembahasan Soal:

Ingat kembali bahwa begin mathsize 14px style left parenthesis g times f right parenthesis left parenthesis x right parenthesis equals g left parenthesis x right parenthesis times f left parenthesis x right parenthesis end style. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 5 g squared times f right parenthesis left parenthesis x right parenthesis end cell equals cell left parenthesis 5 g times g times f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell 5 times g left parenthesis x right parenthesis times g left parenthesis x right parenthesis times f left parenthesis x right parenthesis end cell end table end style

Substitusikan size 14px x size 14px equals size 14px minus size 14px 2, maka

size 14px left parenthesis size 14px 5 size 14px g to the power of size 14px 2 size 14px times size 14px f size 14px right parenthesis begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px equals size 14px 5 size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style.

Akan dicari nilai dari  begin mathsize 14px style f left parenthesis negative 2 right parenthesis end style dan  begin mathsize 14px style g left parenthesis negative 2 right parenthesis end style terlebih dahulu.

Perhatikan bahwa nilai dari begin mathsize 14px style f left parenthesis negative 2 right parenthesis end style adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell size 14px minus fraction numerator size 14px 2 size 14px k over denominator size 14px k begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px minus size 14px 1 end fraction end cell row blank size 14px equals cell size 14px minus fraction numerator size 14px 2 size 14px k over denominator size 14px minus size 14px 2 size 14px k size 14px minus size 14px 1 end fraction end cell row blank size 14px equals cell fraction numerator size 14px 2 size 14px k over denominator size 14px 2 size 14px k size 14px plus size 14px 1 end fraction end cell end table

dan nilai dari undefined adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell square root of size 14px 2 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px plus size 14px 6 end root end cell row blank size 14px equals cell square root of size 14px minus size 14px 4 size 14px plus size 14px 6 end root end cell row blank size 14px equals cell square root of size 14px 2 end cell end table 

Maka, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px left parenthesis size 14px 5 size 14px g to the power of size 14px 2 size 14px times size 14px f size 14px right parenthesis begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell size 14px 5 size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell row size 14px 15 size 14px equals cell size 14px 5 begin mathsize 14px style left parenthesis square root of 2 right parenthesis end style begin mathsize 14px style left parenthesis square root of 2 right parenthesis end style begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row size 14px 15 size 14px equals cell size 14px 5 size 14px times size 14px 2 begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row size 14px 3 size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row cell size 14px 3 begin mathsize 14px style left parenthesis 2 k plus 1 right parenthesis end style end cell size 14px equals cell size 14px 2 size 14px times size 14px 2 size 14px k end cell row cell size 14px 6 size 14px k size 14px plus size 14px 3 end cell size 14px equals cell size 14px 4 size 14px k end cell row cell size 14px 6 size 14px k size 14px minus size 14px 4 size 14px k end cell size 14px equals cell size 14px minus size 14px 3 end cell row cell size 14px 2 size 14px k end cell size 14px equals cell size 14px minus size 14px 3 end cell row size 14px k size 14px equals cell size 14px minus size 14px 3 over size 14px 2 end cell end table 

Sehingga didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px 2 size 14px k size 14px minus size 14px 5 end cell size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis negative 3 over 2 right parenthesis end style size 14px minus size 14px 5 end cell row blank size 14px equals cell size 14px minus size 14px 3 size 14px minus size 14px 5 end cell row blank size 14px equals cell size 14px minus size 14px 8 end cell end table 

Jadi, jawabannya adalah B.

0

Roboguru

Diberikan fungsi  dan . Jika  dan , maka nilai dari  adalah ....

Pembahasan Soal:

Ingat kembali bahwa begin mathsize 14px style left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end style

Oleh karena itu, didapat perhitungan sebagai berikut.

begin mathsize 14px style table row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals f left parenthesis 5 right parenthesis times g left parenthesis 5 right parenthesis end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals open parentheses fraction numerator a minus 2 over denominator square root of 5 plus 4 end root end fraction close parentheses times open parentheses fraction numerator negative 6 times 5 minus 5 over denominator 2 b times 5 plus 5 end fraction close parentheses end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals open parentheses fraction numerator a minus 2 over denominator square root of 9 end fraction close parentheses times open parentheses fraction numerator negative 30 minus 5 over denominator 10 b plus 5 end fraction close parentheses end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals open parentheses fraction numerator a minus 2 over denominator 3 end fraction close parentheses times open parentheses fraction numerator negative 35 over denominator 10 b plus 5 end fraction close parentheses end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals open parentheses fraction numerator a minus 2 over denominator 3 end fraction close parentheses times open parentheses fraction numerator negative 35 over denominator 5 open parentheses 2 b plus 1 close parentheses end fraction close parentheses end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals open parentheses fraction numerator a minus 2 over denominator 3 end fraction close parentheses times open parentheses fraction numerator negative 7 over denominator 2 b plus 1 end fraction close parentheses end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals fraction numerator negative 7 open parentheses a minus 2 close parentheses over denominator 3 left parenthesis 2 b plus 1 right parenthesis end fraction end cell row cell left parenthesis f times g right parenthesis left parenthesis 5 right parenthesis equals fraction numerator negative 7 a plus 14 over denominator 6 b plus 3 end fraction... left parenthesis straight i right parenthesis end cell end table end style


Kemudian, ingat pula bahwa begin mathsize 14px style open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction comma space g left parenthesis x right parenthesis not equal to 0 end style

Oleh karena itu, didapat perhitungan sebagai berikut. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f over g close parentheses left parenthesis 0 right parenthesis end cell equals cell fraction numerator f left parenthesis 0 right parenthesis over denominator g left parenthesis 0 right parenthesis end fraction end cell row cell open parentheses f over g close parentheses left parenthesis 0 right parenthesis end cell equals cell fraction numerator open parentheses begin display style fraction numerator a minus 2 over denominator square root of 0 plus 4 end root end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator negative 6 times 0 minus 5 over denominator 2 b times 0 plus 5 end fraction end style close parentheses end fraction end cell row cell open parentheses f over g close parentheses left parenthesis 0 right parenthesis end cell equals cell fraction numerator open parentheses begin display style fraction numerator a minus 2 over denominator square root of 4 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator negative 5 over denominator 5 end fraction end style close parentheses end fraction end cell row cell open parentheses f over g close parentheses left parenthesis 0 right parenthesis end cell equals cell fraction numerator open parentheses begin display style fraction numerator a minus 2 over denominator 2 end fraction end style close parentheses over denominator open parentheses begin display style negative 1 end style close parentheses end fraction end cell row cell open parentheses f over g close parentheses left parenthesis 0 right parenthesis end cell equals cell negative fraction numerator a minus 2 over denominator 2 end fraction... left parenthesis ii right parenthesis end cell end table end style


Subtitusikan persamaan (i) dan (ii) ke persamaan size 14px 2 begin mathsize 14px style left parenthesis f times g right parenthesis end style begin mathsize 14px style left parenthesis 5 right parenthesis end style size 14px equals size 14px minus size 14px 3 begin mathsize 14px style open parentheses f over g close parentheses end style begin mathsize 14px style left parenthesis 0 right parenthesis end style sehingga diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table row cell 2 open parentheses f times g close parentheses open parentheses 5 close parentheses equals negative 3 open parentheses f over g close parentheses open parentheses 0 close parentheses end cell row cell 2 open parentheses fraction numerator negative 7 a plus 14 over denominator 6 b plus 3 end fraction close parentheses equals negative 3 open parentheses negative fraction numerator a minus 2 over denominator 2 end fraction close parentheses end cell row cell fraction numerator negative 14 a plus 28 over denominator 6 b plus 3 end fraction equals fraction numerator 3 a minus 6 over denominator 2 end fraction end cell row cell 2 left parenthesis negative 14 a plus 28 right parenthesis equals left parenthesis 6 b plus 3 right parenthesis left parenthesis 3 a minus 6 right parenthesis end cell row cell negative 28 a plus 56 equals 18 a b minus 36 b plus 9 a minus 18 end cell row cell negative 18 a b minus 37 a plus 36 b equals negative 74 end cell row cell 18 a b plus 37 a minus 36 b equals 74... left parenthesis iii right parenthesis end cell end table end style


Selanjutnya, dari soal diketahui begin mathsize 14px style negative f left parenthesis 12 right parenthesis plus g left parenthesis 1 right parenthesis equals 0 end style.

Oleh karena itu, didapat perhitungan sebagai berikut.

begin mathsize 14px style table row cell negative f left parenthesis 12 right parenthesis plus g left parenthesis 1 right parenthesis equals 0 end cell row cell negative fraction numerator a minus 2 over denominator square root of 12 plus 4 end root end fraction plus fraction numerator negative 6 times 1 minus 5 over denominator 2 b times 1 plus 5 end fraction equals 0 end cell row cell negative fraction numerator a minus 2 over denominator square root of 16 end fraction plus fraction numerator negative 6 minus 5 over denominator 2 b plus 5 end fraction equals 0 end cell row cell negative fraction numerator a minus 2 over denominator 4 end fraction plus fraction numerator negative 11 over denominator 2 b plus 5 end fraction equals 0 end cell row cell fraction numerator negative 11 over denominator 2 b plus 5 end fraction equals fraction numerator a minus 2 over denominator 4 end fraction end cell row cell negative 44 equals left parenthesis a minus 2 right parenthesis left parenthesis 2 b plus 5 right parenthesis end cell row cell negative 44 equals 2 a b plus 5 a minus 4 b minus 10 end cell row cell negative 34 equals 2 a b plus 5 a minus 4 b... left parenthesis iv right parenthesis end cell end table end style

Jumlahkan persamaan (iii) dan (iv), diperoleh hasil sebagai berikut.

begin mathsize 14px style table attributes columnalign right right right right right columnspacing 0.4em 2px 2px 2px 0.4em end attributes row cell open parentheses iii close parentheses space... end cell cell 18 a b plus end cell cell 37 a minus end cell cell 36 b equals end cell 74 space row cell open parentheses iv close parentheses space... end cell cell 2 a b plus end cell cell 5 a minus end cell cell 4 b equals end cell cell negative 34 end cell plus row space cell 20 a b plus end cell cell 42 a minus end cell cell 40 b equals end cell 40 space row space cell 10 a b plus end cell cell 21 a minus end cell cell 20 b equals end cell 20 space end table end style 

Dengan demikian, nilai dari begin mathsize 14px style 10 a b plus 21 a minus 20 b end style adalah undefined.

Jadi, jawaban yang tepat adalah D.

1

Roboguru

Diketahui  dan . Tentukan: c.

Pembahasan Soal:

begin mathsize 14px style left parenthesis f cross times g right parenthesis left parenthesis negative 1 right parenthesis equals f left parenthesis negative 1 right parenthesis cross times g left parenthesis negative 1 right parenthesis end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 5 end cell equals cell negative 1 end cell row x equals cell negative 6 end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 6 plus 5 right parenthesis end cell equals cell 3 left parenthesis negative 6 right parenthesis squared plus 10 left parenthesis negative 6 right parenthesis – 3 end cell row cell f left parenthesis negative 1 right parenthesis end cell equals cell 108 minus 60 minus 3 end cell row blank equals 45 end table end style
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus 1 end cell equals cell negative 1 end cell row cell 4 x end cell equals 0 row x equals 0 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 4 x – 1 right parenthesis end cell equals cell fraction numerator 1 minus 8 x over denominator 2 x plus 2 end fraction end cell row cell g left parenthesis 4 left parenthesis 0 right parenthesis minus 1 right parenthesis end cell equals cell fraction numerator 1 minus 8 left parenthesis 0 right parenthesis over denominator 2 left parenthesis 0 right parenthesis plus 2 end fraction end cell row cell g left parenthesis negative 1 right parenthesis end cell equals cell 1 half end cell end table end style 


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f cross times g right parenthesis left parenthesis negative 1 right parenthesis end cell equals cell f left parenthesis negative 1 right parenthesis cross times g left parenthesis negative 1 right parenthesis end cell row blank equals cell 45 cross times open parentheses 1 half close parentheses end cell row blank equals cell 45 over 2 end cell end table end style 

0

Roboguru

Perhatikan gambar berikut ini!   Gambar di atas merupakan diagram panah dari fungsi  dan . Nilai dari  dan domain fungsi  secara berturut-turut adalah ...

Pembahasan Soal:

Ingat kembali bahwa size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px times size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis, sehingga diperoleh 

size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px times size 14px g size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px z size 14px times size 14px z size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px z to the power of size 14px 2 

Selanjutnya, untuk menentukan domain size 14px f size 14px times size 14px g, ingat kembali bahwa domain dari size 14px f size 14px times size 14px g adalah irisan dari domain fungsi begin mathsize 14px style f end style dan domain fungsi begin mathsize 14px style g end style, atau begin mathsize 14px style D subscript f times g end subscript equals D subscript f intersection D subscript g end style.

Dari soal, didapat size 14px D subscript size 14px f size 14px equals begin mathsize 14px style left curly bracket 0 comma 1 comma 2 comma 3 right curly bracket end style, dan size 14px D subscript size 14px g size 14px equals begin mathsize 14px style left curly bracket 0 comma 1 comma 4 comma 9 right curly bracket end style. Sehingga size 14px D subscript size 14px f size 14px times size 14px g end subscript size 14px equals size 14px D subscript size 14px f size 14px intersection size 14px D subscript size 14px g size 14px equals begin mathsize 14px style left curly bracket 0 comma space 1 right curly bracket end style.

Maka, nilai dari size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis dan domain fungsi size 14px f size 14px times size 14px g secara berturut-turut adalah begin mathsize 14px style z squared end style dan begin mathsize 14px style open curly brackets 0 comma space 1 close curly brackets end style.

Jadi, jawabannya adalah B.space space space space  

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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