Roboguru

f(x)g(x)h(x)​===​x2+12x−23x+2​  tentukan (f∘(g∘h))(x)=....

Pertanyaan

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell x squared plus 1 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x minus 2 end cell row cell h open parentheses x close parentheses end cell equals cell 3 x plus 2 end cell end table end style 
tentukan open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses open parentheses x close parentheses equals....

  1. begin mathsize 14px style 12 x squared plus 20 x minus 5 end style 

  2. size 14px 16 size 14px x to the power of size 14px 2 size 14px plus size 14px 21 size 14px x size 14px minus size 14px 5 

  3. size 14px 18 size 14px x to the power of size 14px 2 size 14px plus size 14px 22 size 14px x size 14px plus size 14px 5 

  4. size 14px 30 size 14px x to the power of size 14px 2 size 14px plus size 14px 23 size 14px x size 14px plus size 14px 5 

  5. size 14px 36 size 14px x to the power of size 14px 2 size 14px plus size 14px 24 size 14px x size 14px plus size 14px 5 

Pembahasan Video:

Pembahasan Soal:

Diketahui

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell x squared plus 1 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x minus 2 end cell row cell h open parentheses x close parentheses end cell equals cell 3 x plus 2 end cell end table end style

Akan ditentukan open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses open parentheses x close parentheses

Perhatikan perhitungan berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses 3 x plus 2 close parentheses close parentheses end cell row blank equals cell f open parentheses 2 open parentheses 3 x plus 2 close parentheses minus 2 close parentheses end cell row blank equals cell f open parentheses 6 x plus 4 minus 2 close parentheses end cell row blank equals cell f open parentheses 6 x plus 2 close parentheses end cell row blank equals cell open parentheses 6 x plus 2 close parentheses squared plus 1 end cell row blank equals cell 36 x squared plus 24 x plus 4 plus 1 end cell row blank equals cell 36 x squared plus 24 x plus 5 end cell end table end style 

Oleh karena itu, jawaban yang tepat adalah E

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Firmansyah

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui fungsi f:R→R,g:R→R dan h:R→R dengan f(x)=x+2, g(x)=3x−1, dan h(x)=x2−1. Tentukan: b. (g∘h∘f)(x)

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g ring operator left parenthesis h ring operator f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g ring operator open parentheses h left parenthesis f left parenthesis x right parenthesis close parentheses end cell row blank equals cell g ring operator open parentheses left parenthesis x plus 2 right parenthesis squared minus 1 close parentheses end cell row blank equals cell g ring operator open parentheses x squared plus 4 x plus 3 close parentheses end cell row blank equals cell 3 open parentheses x squared plus 4 x plus 3 close parentheses minus 1 end cell row blank equals cell 3 x squared plus 12 x plus 9 minus 1 end cell row blank equals cell 3 x squared plus 12 x plus 8 end cell end table end style 

0

Roboguru

Diketahui f(x)=x+2,g(x)=3x−1 dan h(x)=x2−1. Tentukan rumus fungsi berikut a. (h∘f∘g)(x)

Pembahasan Soal:

Diketahui:

 begin mathsize 14px style f left parenthesis x right parenthesis equals x plus 2 comma space g left parenthesis x right parenthesis equals 3 x minus 1 end stylebegin mathsize 14px style h left parenthesis x right parenthesis equals x squared minus 1 end style

Ditanya:

begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end style = ?

Jawab:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end cell equals cell h open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h open parentheses f open parentheses 3 x minus 1 close parentheses close parentheses end cell row blank equals cell h open parentheses 3 x minus 1 plus 2 close parentheses end cell row blank equals cell open parentheses 3 x plus 1 close parentheses squared minus 1 end cell row blank equals cell 9 x squared plus 6 x plus 1 minus 1 end cell row blank equals cell 9 x squared plus 6 x end cell end table 

Jadi, rumus fungsi begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end style adalah 9 x squared plus 6 x.

 

0

Roboguru

Diketahui fungsi f(x)=x+2, g(x)=3x−1, dan h(x)=x2−1. Tentukan : c. (f∘g∘h)(x) dan (f∘g∘h)(−2)

Pembahasan Soal:

Terlebih dahulu dicari fungsi komposisi begin mathsize 14px style open parentheses g ring operator h close parentheses left parenthesis x right parenthesis end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis h left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g open parentheses x squared minus 1 close parentheses end cell row blank equals cell 3 open parentheses x squared minus 1 close parentheses minus 1 end cell row blank equals cell 3 x squared minus 3 minus 1 end cell row blank equals cell 3 x squared minus 4 end cell end table end style 

Selanjutnya fungsi komposisi begin mathsize 14px style open parentheses g ring operator h close parentheses left parenthesis x right parenthesis end style disubstitusikan ke dalam fungsi size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g ring operator h close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis h left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell f open parentheses 3 x squared minus 4 close parentheses end cell row blank equals cell open parentheses 3 x squared minus 4 close parentheses plus 2 end cell row blank equals cell 3 x squared minus 2 end cell end table end style 

Dengan demikian komposisi dari ketiga fungsi begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses left parenthesis x right parenthesis end style adalah begin mathsize 14px style 3 x squared minus 2 end style

Nilai begin mathsize 14px style x equals negative 2 end style disubstitusikan ke dalam fungsi komposisi sehingga didapatkan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g ring operator h close parentheses left parenthesis negative 2 right parenthesis end cell equals cell 3 times left parenthesis negative 2 right parenthesis squared minus 2 end cell row blank equals cell 12 minus 2 end cell row blank equals 10 end table end style  

Jadi, nilai dari undefined adalah begin mathsize 14px style 10 end style.

0

Roboguru

Diketahui f(x)=5x​−3, g(x)=x1​+2, dan h(x)=3x.  Tentukan: a. nilai dari (f∘g∘h)(91​);

Pembahasan Soal:

 Diketahui :

begin mathsize 14px style f left parenthesis x right parenthesis equals x over 5 minus 3 end style

begin mathsize 14px style g left parenthesis x right parenthesis equals 1 over x plus 2 end style

 begin mathsize 14px style h left parenthesis x right parenthesis equals 3 x end style

nilai dari begin mathsize 14px style left parenthesis f ring operator g ring operator h right parenthesis open parentheses 1 over 9 close parentheses end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses 1 over 9 close parentheses end cell equals cell 3 cross times 1 over 9 equals 1 third end cell row cell g open parentheses 1 third close parentheses end cell equals cell fraction numerator 1 over denominator 1 third end fraction plus 2 equals 5 end cell row cell f open parentheses 5 close parentheses end cell equals cell 5 over 5 minus 3 equals negative 2 end cell row cell open parentheses f ring operator g ring operator h close parentheses open parentheses 1 over 9 close parentheses end cell equals cell f open parentheses g open parentheses h open parentheses 1 over 9 close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses 1 third close parentheses close parentheses end cell row blank equals cell f open parentheses 5 close parentheses end cell row blank equals cell negative 2 end cell end table end style 

Jadi, nilai dari begin mathsize 14px style left parenthesis f ring operator g ring operator h right parenthesis open parentheses 1 over 9 close parentheses end style adalah begin mathsize 14px style negative 2 end style.

0

Roboguru

Diketahui f(x)=x2+2x,g(x)=x−5danh(x)=2−xx−4​. Tentukan (g∘f∘h)(4)

Pembahasan Soal:

Diketahui :


table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis space end cell equals cell space straight x ² space plus space 2 straight x space end cell row cell straight g left parenthesis straight x right parenthesis space end cell equals cell space straight x space minus space 5 space end cell row cell straight h left parenthesis straight x right parenthesis space end cell equals cell space fraction numerator open parentheses straight x minus 4 close parentheses over denominator open parentheses 2 minus straight x close parentheses end fraction end cell end table
 

Ditanya :

Tentukan open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses

Penyelesaian

Akan dicari nilai dari open parentheses f ring operator h close parentheses open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight f open parentheses straight h open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight f open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses squared plus 2 open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 2 straight x minus 8 over denominator 2 minus straight x end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 2 straight x minus 8 open parentheses 2 minus straight x close parentheses over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 4 straight x minus 2 straight x squared minus 16 plus 8 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 minus 2 straight x squared plus 12 straight x minus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell end table

Jadi nilai dari open parentheses f ring operator h close parentheses open parentheses x close parentheses adalah fraction numerator negative x squared plus 4 x over denominator 4 minus 4 x plus x squared end fraction.

Akan dicari nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses tetapi sebelumnya dicari nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell row blank equals cell straight g open parentheses fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction close parentheses end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction minus 5 end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction minus fraction numerator 5 open parentheses negative straight x squared plus 4 straight x close parentheses over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x plus 5 straight x squared minus 20 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator 4 straight x squared minus 20 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell end table

Jadi hasil dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses x close parentheses equals fraction numerator 4 x squared minus 20 x over denominator 4 minus 4 x plus x squared end fraction.

Akan dicari nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses end cell equals cell fraction numerator 4 open parentheses 4 close parentheses squared minus 20 open parentheses 4 close parentheses over denominator 4 minus 4 open parentheses 4 close parentheses plus open parentheses 4 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 16 over denominator 4 end fraction end cell row blank equals cell negative 4 end cell end table

Jadi, nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses equals negative 4.

0

Roboguru

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