Diketahui f(x)=(x+1)/(x-2), g(x)=x+3 , dan h(x)=x^2+2

Diketahui $f (x) = \frac{x + 1}{x - 2},$ $g (x) = x + 3$ , dan $h (x) = x^{2} + 2$ . Fungsi $(f \circ h \circ g) (x) = \dots$

A. $\frac{x^{2} + 16 x + 9}{x^{2} + 6 x + 12}$

B. $\frac{x^{2} + 16 x + 13}{x^{2} + 6 x + 10}$

C. $\frac{x^{2} + 6 x + 15}{x^{2} + 6 x + 9}$

D. $\frac{x^{2} + 6 x + 12}{x^{2} + 6 x + 9}$

E. $\frac{x^{2} + 6 x + 10}{x^{2} + 6 x + 13}$

Penyelesaian

Diketahui:

$f (x) = \frac{x + 1}{x - 2}$

$g (x) = x + 3$

$h (x) = x^{2} + 2$

Ditanya:

$(f \circ h \circ g) (x) = ?$

JAwab

$f (x) = \frac{x + 1}{x - 2}$

$(f \circ h) (x) = \frac{(x^{2} + 2) + 1}{(x^{2} + 2) - 2}$

$(f \circ h) (x) = \frac{x^{2} + 3}{x^{2}}$

$(f \circ h \circ g) (x) = \frac{(x + 3)^{2} + 3}{(x + 3)^{2}}$

$(f \circ h \circ g) (x) = \frac{x^{2} + 6 x + 9 + 3}{x^{2} + 6 x + 9}$

$(f \circ h \circ g) (x) = \frac{x^{2} + 6 x + 12}{x^{2} + 6 x + 9}$

Jawaban : D

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