Pertanyaan

Diketahui f ( x ) = 2 x + 1 x − 6 , x  = − 2 1 , dan g ( x ) = x − 3 .Jika f − 1 adalah invers dari f, maka ( f − 1 ∘ g ) ( x ) adalah...

Diketahui $f (x) = \frac{x - 6}{2 x + 1}$ , $x \neq = - \frac{1}{2}$ , dan $g (x) = x - 3$ . Jika $f^{- 1}$ adalah invers dari f, maka $(f^{- 1} \circ g) (x)$ adalah... $\;$

$fraction numerator x plus 3 over denominator 1 minus 2 x end fraction comma space x not equal to 1 half$
$fraction numerator x plus 3 over denominator 6 minus 2 x end fraction comma space x not equal to 3$
$fraction numerator x plus 3 over denominator 7 minus 2 x end fraction comma space x not equal to 7 over 2$
$fraction numerator x plus 6 over denominator 1 minus 2 x end fraction comma space x not equal to 1 half$
$fraction numerator x plus 6 over denominator 7 minus 2 x end fraction comma space x not equal to 7 over 2$

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Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Oleh karena itu, jawaban yang benar adalah C.

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x minus 6 over denominator 2 x plus 1 end fraction end cell row y equals cell fraction numerator x minus 6 over denominator 2 x plus 1 end fraction end cell row cell y open parentheses 2 x plus 1 close parentheses end cell equals cell x minus 6 end cell row cell 2 x y plus y end cell equals cell x minus 6 end cell row cell y plus 6 end cell equals cell x minus 2 x y end cell row cell y plus 6 end cell equals cell x left parenthesis 1 minus 2 y right parenthesis end cell row x equals cell fraction numerator y plus 6 over denominator 1 minus 2 y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 6 over denominator 1 minus 2 x end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g close parentheses open parentheses x close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator open parentheses open parentheses x minus 3 close parentheses plus 6 close parentheses over denominator open parentheses 1 minus 2 open parentheses x minus 3 close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator x plus 3 over denominator 1 minus 2 x plus 6 end fraction end cell row blank equals cell fraction numerator x plus 3 over denominator 7 minus 2 x end fraction end cell end table$

Oleh karena itu, jawaban yang benar adalah C.