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Pertanyaan

Dari fungsi f colon R rightwards arrow R dan g colon R rightwards arrow R diketahui f open parentheses x close parentheses equals x plus 3 dan open parentheses f ring operator g close parentheses open parentheses x close parentheses equals x squared plus 6 x plus 7, maka g open parentheses x close parentheses equals...

  1. x squared plus 6 x plus 4

  2. x squared minus 6 x plus 4

  3. x squared plus 3 x minus 2

  4. x squared minus 3 x plus 2

  5. x squared plus 6 x minus 4

Pembahasan Soal:

Dengan menggunakan konsep komposisi fungsi diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell x squared plus 6 x plus 7 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell x squared plus 6 x plus 7 end cell row cell g open parentheses x close parentheses plus 3 end cell equals cell x squared plus 6 x plus 7 end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 6 x plus 7 minus 3 end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 6 x plus 4 end cell end table

Dengan demikian maka g open parentheses x close parentheses equals x squared plus 6 x plus 4.

Oleh karena itu, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Nur

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

Diketahui fungsi . Tentukan: a. Invers fungsi  b. Nilai dari

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x plus 2 space dan space left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals 8 x plus 3 end style.

Menentukan begin mathsize 14px style g left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 8 x plus 3 end cell row cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell equals cell 8 x plus 3 end cell row cell g left parenthesis 4 x plus 2 right parenthesis end cell equals cell 8 x plus 3 end cell row blank blank blank end table end style 

Misalkan begin mathsize 14px style a equals 4 x plus 2 space end stylemaka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 2 end cell equals cell 4 x end cell row cell fraction numerator a minus 2 over denominator 4 end fraction end cell equals x end table end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis a right parenthesis end cell equals cell 8 left parenthesis fraction numerator a minus 2 over denominator 4 end fraction right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a minus 2 right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 4 plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 1 end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell end table end style 

Menentukan invers fungsi begin mathsize 14px style g end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell row y equals cell 2 x minus 1 end cell row cell y plus 1 end cell equals cell 2 x end cell row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals x row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell row cell fraction numerator x plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table end style 

a. Jadi, begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator 2 end fraction end style.

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent left parenthesis 7 right parenthesis end cell equals cell fraction numerator 7 plus 1 over denominator 2 end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table end style 

b. Jadi, nilai dari begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4 end style.

0

Roboguru

Fungsi  dan  ditentukan dengan  dan , maka  = ...

Pembahasan Soal:

Menentukan g left parenthesis x right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell g left parenthesis x right parenthesis to the power of negative 1 end exponent end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell fraction numerator 1 over denominator g left parenthesis x right parenthesis end fraction end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x over denominator x minus 3 end fraction semicolon space x not equal to 3 end cell end table 

Menentukan g to the power of negative 1 end exponent left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x over denominator x minus 3 end fraction end cell row y equals cell fraction numerator 2 x over denominator x minus 3 end fraction end cell row cell y left parenthesis x minus 3 right parenthesis end cell equals cell 2 x end cell row cell x y minus 3 y end cell equals cell 2 x end cell row cell x y minus 2 x end cell equals cell 3 y end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals y row x equals cell fraction numerator y over denominator y minus 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator y over denominator y minus 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x over denominator x minus 2 end fraction comma space x not equal to 2 end cell end table 

Dengan demikian, diperoleh g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x over denominator x minus 2 end fraction comma space x not equal to 2.

0

Roboguru

Jika  dan , maka nilai  adalah ....

Pembahasan Soal:

Diberikan fungsi f left parenthesis x right parenthesis equals x squared plus 1 dan fungsi komposisi left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 4 x squared minus 12 x plus 10, fungsi g left parenthesis x right parenthesis dapat dihitung seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f left parenthesis g right parenthesis left parenthesis x right parenthesis end cell equals cell 4 x squared minus 12 x plus 10 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared plus 1 end cell equals cell 4 x squared minus 12 x plus 10 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell 4 x squared minus 12 x plus 10 minus 1 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell 4 x squared minus 12 x plus 9 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell left parenthesis 2 x minus 3 right parenthesis squared end cell row cell g left parenthesis x right parenthesis end cell equals cell square root of left parenthesis 2 x minus 3 right parenthesis squared end root end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell end table

Dengan demikian, fungsi g left parenthesis x right parenthesis adalah 2 x minus 3.

Jadi, jawaban yang terbentuk adalah A.

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Roboguru

Jika  dan , maka ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell space 1 minus 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 4 minus 25 x space end cell row cell negative 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 1 minus 4 minus 25 x space end cell row cell negative 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 25 x minus 5 space end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 5 x plus 1 end cell row cell space g left parenthesis x plus 1 right parenthesis end cell equals cell 5 left parenthesis x plus 1 right parenthesis plus 1 end cell row blank equals cell 5 x plus 5 plus 1 end cell row blank equals cell 5 x plus 6 end cell end table end style 

Jadi, jawaban yang tepat adalah D. 

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Roboguru

Diketahuisuatu fungsi  dan komposisi . Maka fungsi

Pembahasan Soal:

Diketahui:

begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 1 left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 12 x plus 7 end style

Ditanya: begin mathsize 14px style g left parenthesis x right parenthesis end style?

Jawab:

Fungsi komposisi begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style didapat dengan mensubtitusi undefined ke fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 12 x plus 7 end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 12 x plus 7 end cell row cell 4 left parenthesis g left parenthesis x right parenthesis right parenthesis minus 1 end cell equals cell 12 x plus 7 end cell row cell 4 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 12 x plus 8 end cell row cell g left parenthesis x right parenthesis end cell equals cell 3 x plus 2 end cell end table end style
 

Jadi, fungsi begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x plus 2 end style.

0

Roboguru

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