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Jika f(x)=3x−25x+2​, x=32​, maka f−1(x)=....

Pertanyaan

Jika begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 3 x minus 2 end fraction comma space x not equal to 2 over 3 end style, maka begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals.... end style 

  1. begin mathsize 14px style fraction numerator 2 x plus 2 over denominator 3 x plus 5 end fraction comma space x not equal to negative 5 over 3 end style 

  2. begin mathsize 14px style fraction numerator 2 x plus 2 over denominator 5 x minus 5 end fraction comma space x not equal to 1 end style 

  3. begin mathsize 14px style fraction numerator 2 x plus 2 over denominator 3 x minus 5 end fraction comma space x not equal to negative 5 over 3 end style  

  4. begin mathsize 14px style fraction numerator negative 2 x plus 2 over denominator 3 x minus 5 end fraction comma space x not equal to 5 over 3 end style 

  5. undefined 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 3 x minus 2 end fraction comma space x not equal to 2 over 3 end style, maka:

begin mathsize 14px style space space space space space space space space f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 3 x minus 2 end fraction space space space space space space space space space space space space y equals fraction numerator 5 x plus 2 over denominator 3 x minus 2 end fraction y open parentheses 3 x minus 2 close parentheses equals open parentheses 5 x plus 2 close parentheses 3 x y minus 2 y equals 5 x plus 2 3 x y minus 5 x equals 2 plus 2 y x open parentheses 3 y minus 5 close parentheses equals 2 y plus 2 space space space space space space space space space space space space x equals fraction numerator 2 y plus 2 over denominator 3 y minus 5 end fraction space space space space f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 x plus 2 over denominator 3 x minus 5 end fraction end style 

Jadi, jawaban yang benar adalah C.

102

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Cornbibble

Pembahasan tidak menjawab soal

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