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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 begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals end style....

  1. 0,5undefined 

  2. 1,5undefined 

  3. 3,0undefined 

  4. 3,5undefined 

  5. 4,5undefined 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat!

begin mathsize 14px style y equals f left parenthesis x right parenthesis space left right arrow space x equals f to the power of negative 1 end exponent left parenthesis y right parenthesis end style 

Berdasarkan konsep tersebut akan dicari begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis 7 right parenthesis end style 

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 begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 3 end style 

Jadi, jawaban yang tepat adalah C.

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