Diketahui f(x)=x−22x+1. Nilai f−1(7)=....

Pertanyaan

Diketahui $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator x minus 2 end fraction end style$ . Nilai $\style{font-size:14px}{f^{-1}(7)=}$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat!

Berdasarkan konsep tersebut akan dicari

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f left parenthesis x right parenthesis end cell row y equals cell fraction numerator 2 x plus 1 over denominator x minus 2 end fraction end cell row cell x y minus 2 y end cell equals cell 2 x plus 1 end cell row cell x y minus 2 x end cell equals cell 2 y plus 1 end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals cell 2 y plus 1 end cell row x equals cell fraction numerator 2 y plus 1 over denominator y minus 2 end fraction end cell end table end style$

Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 2 y plus 1 over denominator y minus 2 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 7 right parenthesis end cell equals cell fraction numerator 2 left parenthesis 7 right parenthesis plus 1 over denominator 7 minus 2 end fraction end cell row blank equals cell fraction numerator 14 plus 1 over denominator 5 end fraction end cell row blank equals cell 15 over 5 end cell row blank equals 3 end table end style$

Sehingga nilai

Jadi, jawaban yang tepat adalah C.

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