diketahui fungsi f : R-R g: R-R dan h: R-R dengan f(x) = x+7 g(x)= 3-x dan h(x) = x² +2x-3 tentukan (h•g•f) (x)

Fungsi Komposisi

(gof)(x)
= 3 - (x + 7)
= -4 - x

h(x) = x² + 2x - 3 = (x + 3)(x -1)

(hogof)(x)
= h((gof)(x))
= (-4 - x + 3)(-4 - x - 1)
= (-1 - x)(-5 - x)
= 5 + 5x + x + x²
= x² + 6x + 5

f(x) : x+7
g(x) :3-x
h(x) :x^{2} + 2x - 3
(h•g•f) (x) ?
 
 g (f(x)) =g (x+ 7)
=3 - (x+ 7)
= 3-x-7
=-x - 4

(h•g•f) (x) =h {g (f(x))}
=h ( -x - 4 )
=( -x - 4 )^2 +2 (-x - 4 )- 3
= x^2 +8x +16 -2x -8 -3
=x^2 +6x +5