Pertanyaan

Tentukan invers dari fungsi-fungsi berikut a) f ( x ) = 3 x + 6

Tentukan invers dari fungsi-fungsi berikut

a) $f (x) = 3 x + 6$

D. Kusumawardhani

Master Teacher

Jawaban terverifikasi

Jawaban

Invers fungsi adalah

Invers fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 3 straight x plus 6 end style

adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x minus 6 over denominator 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style$

Pembahasan

Diketahui: Ditanya: Penyelesaian: Misalkan: ,maka: Dengan demikian, Invers fungsi adalah

Diketahui: begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 3 straight x plus 6 end style

Ditanya: begin mathsize 14px style straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end style

Penyelesaian:

Misalkan: begin mathsize 14px style straight y equals straight f left parenthesis straight x right parenthesis rightwards arrow straight x equals straight f to the power of negative 1 end exponent left parenthesis straight y right parenthesis end style , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell 3 straight x plus 6 end cell row straight y equals cell 3 straight x plus 6 end cell row cell straight y minus 6 end cell equals cell 3 straight x end cell row cell fraction numerator straight y minus 6 over denominator 3 end fraction end cell equals straight x row cell fraction numerator straight y minus 6 over denominator 3 end fraction end cell equals cell straight f to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell row cell fraction numerator straight x minus 6 over denominator 3 end fraction end cell equals cell straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table end style$

Dengan demikian, Invers fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 3 straight x plus 6 end style adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x minus 6 over denominator 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style$