Pertanyaan

Fungsi f : R → R didefinisikan sebagai f ( x ) = 3 x + 4 2 x − 1 , x  = 4 3 . Invers dari fungsi f adalah f − 1 ( x ) = ....

Fungsi $f : R \to R$ didefinisikan sebagai $f (x) = \frac{2 x - 1}{3 x + 4}, x \neq = \frac{3}{4}$ . Invers dari fungsi $f$ adalah $f^{- 1} (x) = ....$

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

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Klaim

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Dengan syarat, Jadi, jawaban yang tepat adalah C.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 1 over denominator 3 x plus 4 end fraction end cell row y equals cell fraction numerator 2 x minus 1 over denominator 3 x plus 4 end fraction end cell row cell y open parentheses 3 x plus 4 close parentheses end cell equals cell 2 x minus 1 end cell row cell 3 x y plus 4 y end cell equals cell 2 x minus 1 end cell row cell 3 x y minus 2 x end cell equals cell negative 1 minus 4 y end cell row cell x open parentheses 3 y minus 2 close parentheses end cell equals cell negative 1 minus 4 y end cell row x equals cell fraction numerator negative 1 minus 4 y over denominator 3 y minus 2 end fraction times fraction numerator negative 1 over denominator negative 1 end fraction end cell row x equals cell fraction numerator 4 y plus 1 over denominator 2 minus 3 y end fraction end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x plus 1 over denominator 2 minus 3 x end fraction end cell row blank blank blank end table end style$

Dengan syarat,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 minus 3 x end cell not equal to 0 row cell negative 3 x end cell not equal to cell negative 2 end cell row x not equal to cell fraction numerator negative 2 over denominator negative 3 end fraction end cell row x not equal to cell 2 over 3 end cell row blank blank blank end table end style$

Jadi, jawaban yang tepat adalah C.