Pertanyaan

Tentukan invers dari fungsi-fungsi berikut c) f ( x ) = 2 x + 1 2 − x

Tentukan invers dari fungsi-fungsi berikut

c) $f (x) = \frac{2 - x}{2 x + 1}$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Pembahasan

Invers fungsi rasional. Diketahui: Ditanya: Penyelesaian: Misalkan: Maka: Jadi, Invers fungsi adalah

Invers fungsi rasional.

Diketahui:

$begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 2 minus straight x over denominator 2 straight x plus 1 end fraction end style$

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:

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

Jadi, Invers fungsi $begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 2 minus straight x over denominator 2 straight x plus 1 end fraction end style$ adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 minus straight x over denominator 2 straight x plus 1 end fraction end cell end table end style$