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

Diketahui $f (x) = 3 - x$ , $g (x) = x^{2} + 2 x - 5$ , dan $h (x) = 2 x + 1$ . Nilai $(g \circ h \circ f) (2) = \dots$

A. 5

B. 10

C. 15

D. 20

E. 25

Penyelesaian

Diketahui:

$f (x) = 3 - x$

$g (x) = x^{2} + 2 x - 5$

$h (x) = 2 x + 1$

Ditanya:

$(g \circ h \circ f) (2) = ?$

Jawab

$g (x) = x^{2} + 2 x - 5$

$(g \circ h) (x) = (2 x + 1)^{2} + 2 (2 x + 1) - 5$

$(g \circ h) (x) = 4 x^{2} + 4 x + 1 + 4 x + 2 - 5$

$(g \circ h) (X) = 4 x^{2} + 8 x - 2$

$(g \circ h \circ f) (x) = 4 (3 - x)^{2} + 8 (3 - x) - 2$

$(g \circ h \circ f) (x) = 4 (9 - 6 x + x^{2}) + 24 - 8 x - 2$

$(g \circ h \circ f) (x) = 36 - 24 x + 4 x^{2} + 24 - 8 x - 2$

$(g \circ h \circ f) (x) = 4 x^{2} - 32 x + 58$

$(g \circ h \circ f) (2) = 4 (2)^{2} - 32 (2) + 58$

$(g \circ h \circ f) (2) = 16 - 64 + 58 = 10$

Jawaban : B

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