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

Diketahui fungsi $f (x) = x + 1$ , $g (x) = x^{2} - 5 x - 3$ , dan $h (x) = 3 x - 1$ . Tentukan:

a. $(f \circ g \circ h) (x)$

b. $(g \circ h \circ f) (x)$

Jawab

a. $(f \circ g \circ h) (x)$

$f (x) = x + 1$

$(f \circ g) (x) = (x^{2} - 5 x - 3) + 1$

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

$(f \circ g \circ h) (x) = (3 x - 1)^{2} - 5 (3 x - 1) - 2$

$(f \circ g \circ h) (x) = 9 x^{2} - 6 x + 1 - 15 x + 5 - 2$

$(f \circ g \circ h) (x) = 9 x^{2} - 21 x + 4$

b. $(g \circ h \circ f) (x)$

$g (x) = x^{2} - 5 x + 3$

$(g \circ h) (x) = (3 x - 1)^{2} - 5 (3 x - 1) + 3$

$(g \circ h) (x) = 9 x^{2} - 6 x + 1 - 15 x + 5 + 3$

$(g \circ h) (x) = 9 x^{2} - 21 x + 9$

$(g \circ h \circ f) (x) = 9 (x + 1)^{2} - 21 (x + 1) + 9$

$(g \circ h \circ f) (x) = 9 (x^{2} + 2 x + 1) - 21 x - 21 + 9$

$(g \circ h \circ f) (x) = 9 x^{2} + 18 x + 9 - 21 x - 21 + 9$

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

      
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