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Pertanyaan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 8 x minus 4 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 12 plus 6 x end style. Maka tentukan:

a. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style 

b. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end style 

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell 5 over 16 end cell end table end style.

Pembahasan

Diketahui:

begin mathsize 14px style f left parenthesis x right parenthesis equals 8 x minus 4 g left parenthesis x right parenthesis equals 12 plus 6 x end style

Ditanya: 

a. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style

b. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end style 

Jawab:

a. Akan dicari fungsi komposisi dari begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style terlebih dahulu.
 

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 g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 12 plus 6 left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 12 plus 6 left parenthesis 8 x minus 4 right parenthesis end cell row blank equals cell 12 plus 48 x minus 24 end cell row blank equals cell 48 x minus 12 end cell end table end style
 

Didapat begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals 48 x minus 12 end style, fungsi inversnya:
 

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 48 x minus 12 end cell row y equals cell 48 x minus 12 end cell row cell 48 x end cell equals cell y plus 12 end cell row x equals cell fraction numerator y plus 12 over denominator 48 end fraction rightwards double arrow left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 12 over denominator 48 end fraction end cell end table end style
 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 12 over denominator 48 end fraction end cell end table end style.

 

b. Akan disubtitusi nilai begin mathsize 14px style x equals 3 end style ke fungsi begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table 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 to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 12 over denominator 48 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell fraction numerator 3 plus 12 over denominator 48 end fraction end cell row blank equals cell 15 over 48 end cell row blank equals cell 5 over 16 end cell end table end style
 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell 5 over 16 end cell end table end style.

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