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Nilai fungsi invers f−1(2) dari f(x)=2x−13x+4​, x=21​ .

Pertanyaan

Nilai fungsi invers begin mathsize 14px style straight f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end style dari begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction comma space straight x not equal to 1 half space end style.

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Jika begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction comma space straight x not equal to 1 half space end style maka begin mathsize 14px style straight f to the power of negative 1 end exponent left parenthesis 2 right parenthesis equals 6 end style.

Pembahasan

Diketahui:

begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction comma space straight x not equal to 1 half space end style

Dengan menerapkan konsep invers fungsi,

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 sehingga diperoleh:

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 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction end cell row straight y equals cell fraction numerator 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction end cell row cell straight y left parenthesis 2 straight x minus 1 right parenthesis end cell equals cell 3 straight x plus 4 end cell row cell 2 yx minus straight y end cell equals cell 3 straight x plus 4 end cell row cell 2 yx minus 3 straight x end cell equals cell straight y plus 4 end cell row cell straight x left parenthesis 2 straight y minus 3 right parenthesis end cell equals cell straight y plus 4 end cell row straight x equals cell fraction numerator straight y plus 4 over denominator left parenthesis 2 straight y minus 3 right parenthesis 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 straight y plus 4 over denominator left parenthesis 2 straight y minus 3 right parenthesis end fraction end cell row cell straight f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell fraction numerator 2 plus 4 over denominator 2 times 2 minus 3 end fraction end cell row blank equals cell fraction numerator 6 over denominator 4 minus 3 end fraction end cell row blank equals cell 6 over 1 end cell row blank equals 6 end table end style 

Jadi, Jika begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 straight x minus 1 end fraction comma space straight x not equal to 1 half space end style maka begin mathsize 14px style straight f to the power of negative 1 end exponent left parenthesis 2 right parenthesis equals 6 end style.

103

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