( g o f) (x) = (x- 1) ² . g ( x) = x + 5 tentukan f(x) dan (f o g) ( x)

jawab


gof(x) =  (x -1)^2
g (f(x))  = (x -1)^2
f(x) + 5 = (x-1)^2

f(x) = (x -1)^2 + 5

fog(x) = f { g(x)} = f {x+5)
= (x +5-1)^2 +5
= (x+4)^2 + 5

(g o f) (x) = x^2 -2x +1
g(f(x)) = x^2 -2x + 1
f(x) + 5 = x^2 -2x +1
f(x) = x^2 -2x - 4

f o g (x)
f(g(x))
(x + 5)^2 - 2(x + 5) -4
x^2 + 10x + 25 - 2x - 10 -4
x^2 + 8x + 11