Jika f(x)=2x+3, g(x)=x^2+4x+1, dan h(x)=x-5

Jika $f (x) = 2 x + 3$ , $g (x) = x^{2} + 4 x + 1$ , dan $h (x) = x - 5$ , fungsi komposisi $(f \circ g \circ h) (x) = \dots$

A. $4 x^{2} + 8 x - 17$

B. $4 x^{2} - 10 x + 13$

C. $4 x^{2} - 12 x - 5$

D. $2 x^{2} - 12 x + 15$

E. $2 x^{2} + 10 x - 11$

Penyelesaian

Diketahui:

$f (x) = 2 x + 3$

$g (x) = x^{2} + 4 x + 1$

$h (x) = x - 5$

Ditanya:

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

Jawab

$f (x) = 2 x + 3$

$(f \circ g) (x) = 2 (x^{2} + 4 x + 1) + 3$

$(f \circ g) (x) = 2 x^{2} + 8 x + 2 + 3)$

$(f \circ g) (x) = 2 x^{2} + 8 x + 5$

$(f \circ g \circ h) (x) = 2 (x - 5)^{2} + 8 (x - 5) + 5$

$(f \circ g \circ h) (x) = 2 (x^{2} - 10 x + 25) + 8 x - 40 + 5$

$(f \circ g \circ h) (x) = 2 x^{2} - 20 x + 50 + 8 x - 35$

$(f \circ g \circ h) (x) = 2 x^{2} - 12 x + 15$

Jawaban : D

Muda Berkarya Intelektual Normatif

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