Question

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

g(x)=x+3
h(x)=2x^2
Write the expressions for :
(g-h)(x)
and
(g+h)(x)
and evaluate (g*h)(-3)

Answer 1

The expressions for (g-h)(x) and (g+h)(x) are -2x^2 + x + 3 and 2x^2 + x + 3, respectively. The value of (g*h)(-3) is 0.

Step-by-step explanation:

To find the expressions for (g-h)(x) and (g+h)(x), we need to subtract and add the functions g(x) and h(x) respectively.

(g-h)(x) = g(x) - h(x) = (x+3) - (2x^2) = -2x^2 + x + 3

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

To evaluate (g*h)(-3), we need to multiply the values of g(-3) and h(-3).

g(-3) = -3 + 3 = 0

h(-3) = 2(-3)^2 = 18

(g*h)(-3) = g(-3) * h(-3) = 0 * 18 = 0