Product of two functions

Question

Suppose that the functions g and h are defined for all real numbers x as follows.

g(x)=x+1

h(x)=2x²

Write the expressions for (g h)(x) and (g-h)(x) and evaluate (g+h)(−2).

(g h)(x)=

(g-h)(x)=

(g+h)(-2)=

Answer 1

g+h = 2x^2 + x + 1

g - h = 2x^2 -x -1

g*h = 2x^2(x+1) = 2x^3 + 2x^2

(g+h)(-2) = 2(-2)^2 + -2 + 1 = 2(4) + -2 + 1 = 8-2+1 = 7

(g-h)(-2) = 2(-2)^2 - (-2) - 1 = 2(4) + 2 - 1 = 8+2-1 = 9