Diketahui Fungsi f(x)=(x+2)/(x-5) dan g(x)=2x+3, Maka (g ∘ f)^-1(x)=

Diketahui fungsi $f (x) = \frac{x + 2}{x - 5}$ dan $g (x) = 2 x + 3$ , maka $(g \circ f)^{- 1} (x) =$ ...

A. $\frac{5 x + 11}{x - 5}$

B. $\frac{5 x - 1}{x + 11}$

C. $\frac{5 x - 11}{x - 5}$

D. $\frac{x - 5}{5 x - 11}$

E. $\frac{x + 5}{5 x - 11}$

Diketahui:

$f (x) = \frac{x + 2}{x - 5}$

$g (x) = 2 x + 3$

Ditanya: $(g \circ f)^{- 1} (x) =$

Jawab

$(g \circ f) (x) = 2 (\frac{x + 2}{x - 5}) + 3$

$(g \circ f) (x) = \frac{2 x + 4}{x - 5} + 3$

$(g \circ f) (x) = \frac{2 x + 4}{x - 5} + \frac{3 (x - 5)}{x - 5}$

$(g \circ f) (x) = \frac{2 x + 4 + 3 x - 15}{x - 5}$

$(g \circ f) (x) = \frac{5 x - 11}{x - 5}$

Cara 1

misal $(g \circ f) (x) = y$

$\frac{5 x - 11}{x - 5} = y$

$(5 x - 11) = y (x - 5)$

$5 x - 11 = y x - 5 y$

$5 y - 11 = y x - 5 x$

$5 y - 11 = x (y - 5)$

$\frac{5 y - 11}{y - 5} = x$

$(g \circ f)^{- 1} (x) = \frac{5 x - 11}{x - 5}$

Cara 2

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

$(g \circ f) (x) = \frac{5 x - 11}{x - 5}$

$(g \circ f)^{- 1} (x) = \frac{5 x - 11}{x - 5}$

Jawaban : C

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