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Diketahui fungsi f(x)=x+32x−5​,x=3dan g(x)=x2​. Fungsi (f∘g)−1(x) adalah ...

Pertanyaan

Diketahui fungsi f left parenthesis x right parenthesis equals fraction numerator 2 x minus 5 over denominator x plus 3 end fraction comma space x not equal to 3 spacedan g left parenthesis x right parenthesis equals 2 over x. Fungsi left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis adalah ...  

  1. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 minus 2 x over denominator 3 x plus 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table 

  2. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 minus 2 x over denominator 3 x minus 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table 

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 minus 4 x over denominator 3 x plus 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table 

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 plus 4 x over denominator 3 x plus 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table 

  5. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x plus 5 over denominator 2 x minus 4 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table 

Pembahasan:

Menentukan f to the power of negative 1 end exponent left parenthesis x right parenthesis space:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell y rightwards arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis equals x end cell row y equals cell fraction numerator 2 x minus 5 over denominator x plus 3 end fraction end cell row cell y x plus 3 y end cell equals cell 2 x minus 5 end cell row cell y x minus 2 x end cell equals cell negative 3 y minus 5 end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals cell negative 3 y minus 5 end cell row x equals cell fraction numerator negative 3 y minus 5 over denominator y minus 2 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator negative 3 y minus 5 over denominator y minus 2 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator negative 3 x minus 5 over denominator x minus 2 end fraction comma space x not equal to 2 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 y rightwards arrow g to the power of negative 1 end exponent left parenthesis y right parenthesis equals x end cell row blank blank blank row y equals cell 2 over x end cell row x equals cell 2 over y end cell row cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell 2 over y end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell 2 over x end cell row blank blank blank end table 

Menentukan left parenthesis f ring operator g right parenthesis 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 left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell left parenthesis g to the power of negative 1 end exponent ring operator space f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g to the power of negative 1 end exponent left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g to the power of negative 1 end exponent open parentheses fraction numerator negative 3 x minus 5 over denominator x minus 2 end fraction close parentheses end cell row blank equals cell fraction numerator 2 over denominator fraction numerator negative 3 x minus 5 over denominator x minus 2 end fraction end fraction end cell row blank equals cell fraction numerator 2 left parenthesis x minus 2 right parenthesis over denominator negative 3 x minus 5 end fraction end cell row blank equals cell fraction numerator 2 x minus 4 over denominator negative 3 x minus 5 end fraction end cell row blank equals cell fraction numerator 4 minus 2 x over denominator 3 x plus 5 end fraction comma space x not equal to negative 5 over 3 end cell end table 

Oleh karena itu, jawaban yang benar adalah A.

Jawaban terverifikasi

Dijawab oleh:

O. Rahmawati

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 06 Oktober 2021

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