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Pertanyaan

Diketahui fungsi begin mathsize 14px style straight f colon straight R rightwards arrow straight R end style, dengan begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end style. Invers fungsi begin mathsize 14px style f end style adalah 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 4 x plus 1 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style 

  2. begin mathsize 14px style fraction numerator 2 x minus 1 over denominator 4 x plus 1 end fraction comma space x not equal to fraction numerator negative 1 over denominator 4 end fraction end style 

  3. begin mathsize 14px style fraction numerator x minus 1 over denominator 2 x plus 4 end fraction comma space x not equal to negative 2 end style 

  4. begin mathsize 14px style fraction numerator 4 x plus 1 over denominator x minus 1 end fraction comma space x not equal to 1 end style 

  5. begin mathsize 14px style fraction numerator 2 x plus 4 over denominator x minus 1 end fraction comma space x not equal to 1 end style 

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Diketahui fungsi begin mathsize 14px style straight f colon straight R rightwards arrow straight R end style, dengan begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end style. Maka:

begin mathsize 14px style space space space space space space space space f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 x minus 4 end fraction space space space space space space space space space space space space y equals fraction numerator x plus 1 over denominator 2 x minus 4 end fraction y open parentheses 2 x minus 4 close parentheses equals x plus 1 space 2 x y minus 4 y equals x plus 1 space space space 2 x y minus x equals 1 plus 4 y x open parentheses 2 y minus 1 close parentheses equals 4 y plus 1 space space space space space space space space space space space space x equals fraction numerator 4 y plus 1 over denominator 2 y minus 1 end fraction space space space space space f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 4 x plus 1 over denominator 2 x minus 1 end fraction end style 

Oleh karena itu, jawaban yang benar adalah A.

25

5.0 (2 rating)

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