Question

Given: f(x) = 2x + 5 and g(x) = x2 and h(x) = -2x

h(g(f(x))) =


I have the answers already but I really don't understand so I'm primarily in this for the explanation and work please!

Thank you <3

Answer 1

• h(g(f(x))) = -8x² - 40x - 50

Explanation:

Given:

• f(x) = 2x + 5
• g(x) = x²
• h(x) = -2x

To find h(g(f(x))) first find g(f(x)), substitute x with f(x):

• g(f(x)) = g(2x + 5)

Since g(x) = x², the value of g(2x + 5) is:

• g(f(x)) = (2x + 5)²

Now, the next step:

• h(g(f(x))) = h((2x + 5)²) = -2(2x + 5)² = -8x² - 40x - 50