Question

Using the functions f(x) = 2x + 7, g(x) = x2 - 4, and h(x) = 5x. Find all of the following. Make sure your answer is in simplest form. a. 4h(x) b. f(x) - g(x) c. f(g(x)) d. g(x)h(x) e. g(x) / f(x)

Answer 1

Given

f(x) = 2x+7

g(x) = x^2-4

h(x) = 5x

a. 4h(x)

= 4 * 5x

= 20x

b. f(x) - g(x)

f(x) - g(x) = 2x + 7 - (x^2 - 4)

= 2x+7-x^2+4

=-x^2+2x+7+4

=-x^2+2x+11

c. f(g(x)) = 2(g(x))+7

=2(x^2-4) +7

=2x^2-8+7

=2x^2-1

d. g(x)h(x) = (x^2-4)(5x)

= 5x^3 - 20x

e. g(x) / f(x) = x2 - 4/ 2x + 7