Jika f(x)=x+29x+17, x=−2 maka nilai f−1(10) adalah ....

Pertanyaan

Jika $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end style$ , $\style{font-size:14px}{x\neq-2}$ maka nilai $\style{font-size:14px}{f^{-1}\left(10\right)}$ adalah ....

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

nilai

adalah

Pembahasan

Dengan menerapkan konsep invers fungsi diperoleh perhitungan sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end cell row y equals cell fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end cell row cell y open parentheses x plus 2 close parentheses end cell equals cell 9 x plus 17 end cell row cell x y plus 2 y end cell equals cell 9 x plus 17 end cell row cell x y minus 9 x end cell equals cell negative 2 y plus 17 end cell row cell x open parentheses y minus 9 close parentheses end cell equals cell negative 2 y plus 17 end cell row x equals cell fraction numerator negative 2 y plus 17 over denominator y minus 9 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 17 over denominator x minus 9 end fraction end cell end table end style$

Selanjutnya, dengan cara substitusi diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 17 over denominator x minus 9 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses 10 close parentheses end cell equals cell fraction numerator negative 2 open parentheses 10 close parentheses plus 17 over denominator 10 minus 9 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 1 end fraction end cell row blank equals cell negative 3 end cell end table end style$

Jadi, nilai adalah .