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Pertanyaan

Jika begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight x minus 4 end style dan begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight x squared minus 5 straight x plus 2 end style, fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals.... end style 

  1. begin mathsize 14px style straight x squared plus 2 straight x minus 1 end style 

  2. Error converting from MathML to accessible text. 

  3. Error converting from MathML to accessible text. 

  4. Error converting from MathML to accessible text. 

  5. Error converting from MathML to accessible text. 

Pembahasan Soal:

Diketahui: 

begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight x minus 4 end style dan begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight x squared minus 5 straight x plus 2 end style,

Ditanya:

fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals.... end style 

Jawab,

Dengan menerapkan konsep fungsi komposisi, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis end cell equals cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end cell row cell straight f left parenthesis straight x minus 4 right parenthesis end cell equals cell straight x squared minus 5 straight x plus 2 end cell end table end style 

Misalkan begin mathsize 14px style straight y equals straight x minus 4 rightwards arrow straight x equals straight y plus 4 end style, nilai begin mathsize 14px style y end style dan begin mathsize 14px style x end style kita substitusi ke begin mathsize 14px style straight f left parenthesis straight x minus 4 right parenthesis equals straight x squared minus 5 straight x plus 2 end style sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x minus 4 right parenthesis end cell equals cell straight x squared minus 5 straight x plus 2 end cell row cell straight f left parenthesis straight y right parenthesis end cell equals cell left parenthesis straight y plus 4 right parenthesis squared minus 5 left parenthesis straight y plus 4 right parenthesis plus 2 end cell row blank equals cell straight y squared plus 8 straight y plus 16 minus 5 straight y minus 20 plus 2 end cell row blank equals cell straight y squared plus 3 straight y minus 2 end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight x squared plus 3 straight x minus 2 end cell end table end style 

Jadi, Jika begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight x minus 4 end style dan begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight x squared minus 5 straight x plus 2 end style maka Error converting from MathML to accessible text..

Oleh karena itu, Jawaban yang benar adalah D

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 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.

0

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

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