Pertanyaan

Diketahui g ( x ) = 2 x + 5 − 3 x + 4 , x  = − 2 5 , jika g − 1 adalah invers fungsi g , fungsi g − 1 ( x − 3 ) = …

Diketahui $g (x) = \frac{- 3 x + 4}{2 x + 5}, x \neq = - \frac{5}{2},$ jika $g^{- 1}$ adalah invers fungsi $g,$ fungsi $g^{- 1} (x - 3) = \dots$

$fraction numerator negative 5 x plus 19 over denominator 2 x minus 3 end fraction$
$fraction numerator negative 5 x plus 7 over denominator 2 x minus 3 end fraction$
$fraction numerator negative 5 x plus 19 over denominator 2 x plus 3 end fraction$
$fraction numerator negative 4 x plus 15 over denominator 2 x plus 3 end fraction$
$fraction numerator negative 4 x plus 15 over denominator 2 x minus 3 end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat rumus invers fungsi rasional! f ( x ) f − 1 ( x ) = = c x + d a x + b c x − a − d x + b Nilai g ( x ) = 2 x + 5 − 3 x + 4 , x  = − 2 5 , maka a = − 3 , b = 4 , c = 2 dan d = 5 . Mencari nilai Mencari nilai dari Jadi,fungsi g − 1 ( x − 3 ) adalah . Oleh karena itu, jawaban yang benar adalah A.

Ingat rumus invers fungsi rasional!

$f (x) f^{- 1} (x) = = \frac{a x + b}{c x + d} \frac{- d x + b}{c x - a}$

Nilai $g (x) = \frac{- 3 x + 4}{2 x + 5}, x \neq = - \frac{5}{2},$ maka $a = - 3$ , $b = 4$ , $c = 2$ dan $d = 5$ . Mencari nilai g to the power of negative 1 end exponent left parenthesis x right parenthesis

$g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 5 x plus 4 over denominator 2 x plus 3 end fraction$

Mencari nilai dari g to the power of negative 1 end exponent left parenthesis x minus 3 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent left parenthesis x minus 3 right parenthesis end cell equals cell fraction numerator negative 5 x plus 4 over denominator 2 x plus 3 end fraction end cell row blank equals cell fraction numerator negative 5 left parenthesis x minus 3 right parenthesis plus 4 over denominator 2 left parenthesis x minus 3 right parenthesis plus 3 end fraction end cell row blank equals cell fraction numerator negative 5 x plus 15 plus 4 over denominator 2 x minus 6 plus 3 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x minus 3 right parenthesis end cell equals cell fraction numerator negative 5 x plus 19 over denominator 2 x minus 3 end fraction end cell end table$

Jadi, fungsi $g^{- 1} (x - 3)$ adalah $fraction numerator negative 5 x plus 19 over denominator 2 x minus 3 end fraction$ .