Given fx x 2 and g x x2 2x find the following f degree g

Given f(x) = x + 2 and g (x) = x^2 + 2x, find the following: (f degree g) (x) f (x) = x + 2 9 (x) = x^2 + 2x g(x + h) - g (x)/h (f o y) x = x^2 + 2x fx (x +)^2 + 2 (x + 2) x^2 + 4 + 2x + 4 x^2 + 8 x^2 + 2x

Solution

f(x) = x+2

g(x) = x^2 + 2x

a) (fog)(x)

plug g(x) into f(x)

(fog)(x) = (x*2+2x) + 2 = x^2 + 2x + 2

b) { g(x+h) - g(x) } / h

g(x+h) = (x+h)^2 + 2(x+h) = x^2 +2hx +h^2 + 2x + 2hx = x^2 + 4hx + 2x + h^2

plugging the values in the formula

{ g(x+h) - g(x) } / h = {x^2 + 4hx + 2x + h^2 - x^2 - 2x } /h

{ g(x+h) - g(x) } / h = h + 4x