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Diketahui f(x)=1−x1​1+x1​​. Nilai f−1(5)=....

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 plus begin display style 1 over x end style over denominator 1 minus begin display style 1 over x end style end fraction end style. Nilai begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis 5 right parenthesis equals end style....

  1. begin mathsize 14px style 3 end style 

  2. begin mathsize 14px style 5 over 2 end style 

  3. begin mathsize 14px style 2 end style 

  4. begin mathsize 14px style 3 over 2 end style 

  5. undefined 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat!

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

Berdasarkan konsep tersebut akan dicari nilai begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis 5 right parenthesis equals... 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 1 plus begin display style 1 over x end style over denominator 1 minus begin display style 1 over x end style end fraction end cell row cell y minus y over x end cell equals cell 1 plus 1 over x end cell row cell y minus 1 end cell equals cell 1 over x plus y over x end cell row cell y minus 1 end cell equals cell 1 over x left parenthesis 1 plus y right parenthesis end cell row cell fraction numerator y minus 1 over denominator y plus 1 end fraction end cell equals cell 1 over x end cell row cell fraction numerator y plus 1 over denominator y minus 1 end fraction end cell equals x end table end style 

Dengan demikian begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis y right parenthesis equals fraction numerator y plus 1 over denominator y minus 1 end fraction end style, maka nilai dari 

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 5 right parenthesis end cell equals cell fraction numerator 5 plus 1 over denominator 5 minus 1 end fraction end cell row blank equals cell 6 over 4 end cell row blank equals cell 3 over 2 end cell end table end style 

Jadi, jawaban yang tepat adalah D.

66

4.6 (3 rating)

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