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 stylebegin mathsize 14px style x not equal to negative 2 end style maka nilai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah ....

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 3 end table.

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 begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 3 end table.

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