Pertanyaan

Ditentukan f ( x ) = 3 − 4 x 7 x − 5 , x  = 4 3 dan f − 1 ( x ) merupakan invers dari f ( x ) , fungsi f − 1 ( 2 x − 4 ) adalah ....

Ditentukan $f (x) = \frac{7 x - 5}{3 - 4 x}$ , $x \neq = \frac{3}{4}$ dan $f^{- 1} (x)$ merupakan invers dari $f (x)$ , fungsi $f^{- 1} (2 x - 4)$ adalah ....

$begin mathsize 14px style fraction numerator 21 minus 8 x over denominator 14 x minus 31 end fraction comma space x not equal to 31 over 14 end style$
$begin mathsize 14px style fraction numerator 14 x minus 33 over denominator 19 minus 8 x end fraction comma space x not equal to 19 over 8 end style$
$begin mathsize 14px style fraction numerator 3 x plus 5 over denominator 4 x plus 7 end fraction comma space x not equal to negative 7 over 4 end style$
$begin mathsize 14px style fraction numerator 6 x minus 7 over denominator 8 x minus 9 end fraction comma space x not equal to 9 over 8 end style$
$begin mathsize 14px style fraction numerator 5 minus 4 x over denominator 7 x minus 3 end fraction comma space x not equal to 3 over 7 end style$

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Klaim

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Diketahui fungsi , . Maka: Sehinggafungsi dapat ditentukan sebagai berikut: Jadi, jawaban yang tepat adalah D.

Diketahui fungsi $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 7 x minus 5 over denominator 3 minus 4 x end fraction end style$ , . Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x minus 5 over denominator 3 minus 4 x end fraction end cell row y equals cell fraction numerator 7 x minus 5 over denominator 3 minus 4 x end fraction space end cell row cell y left parenthesis 3 minus 4 x right parenthesis end cell equals cell 7 x minus 5 end cell row cell 3 y minus 4 x y end cell equals cell 7 x minus 5 end cell row cell 3 y plus 5 end cell equals cell 7 x plus 4 x y end cell row cell 3 y plus 5 end cell equals cell x left parenthesis 7 plus 4 y right parenthesis end cell row cell fraction numerator 3 y plus 5 over denominator left parenthesis 7 plus 4 y right parenthesis end fraction end cell equals x row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 5 over denominator left parenthesis 7 plus 4 x right parenthesis end fraction end cell end table$

Sehingga fungsi dapat ditentukan sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 5 over denominator left parenthesis 7 plus 4 x right parenthesis end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 2 x minus 4 right parenthesis end cell equals cell fraction numerator 3 left parenthesis 2 x minus 4 right parenthesis plus 5 over denominator left parenthesis 7 plus 4 left parenthesis 2 x minus 4 right parenthesis right parenthesis end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 2 x minus 4 right parenthesis end cell equals cell fraction numerator 6 x minus 12 plus 5 over denominator left parenthesis 7 plus 8 x minus 16 right parenthesis end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 2 x minus 4 right parenthesis end cell equals cell fraction numerator 6 x minus 7 over denominator 8 x minus 9 end fraction end cell end table$

Jadi, jawaban yang tepat adalah D.