Question

Given: F(x) = 2x + 5 and g(x) = x^2 and h(x) = -2x

H(g(f(x))) = ?

Answer 1

H(g(f(x))) = -8x^2 - 40x - 50

Explanation:

First, you find f(x) by plugging F(x) into the expression for f(x):

f(x) = 2x + 5

Next, you find g(f(x)) by plugging f(x) into the expression for g(x):

g(f(x)) = (2x + 5)^2

Expanding this expression gives:

g(f(x)) = 4x^2 + 20x + 25

Finally, you find h(g(f(x))) by plugging g(f(x)) into the expression for h(x):

h(g(f(x))) = -2(4x^2 + 20x + 25)

Simplifying this expression gives:

h(g(f(x))) = -8x^2 - 40x - 50

Therefore, H(g(f(x))) = -8x^2 - 40x - 50.