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Tentukan f−1(x) dari f(x)=x−2x+1​.

Pertanyaan

Tentukan begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis end style dari begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator x minus 2 end fraction end style.

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawabannya yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis 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 x plus 1 over denominator x minus 1 end fraction end cell end table end style.

Pembahasan

Dengan menggunakan konsep invers fungsi, maka didapatkan:

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

Jadi, jawabannya yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis 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 x plus 1 over denominator x minus 1 end fraction end cell end table end style.

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