Question

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

h(g(f(x))) = ?x²+ ?x + ?

Answer 1

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

Explanation:

We have:

h(x) = -2x

g(x) = x^2

f(x) = 2x + 5

So, we can replace the respective value:

h(g(f(x)))

first substituting the value of f(x) in x of g(x).

h(g(2x + 5))

second, substituting the value of g(x) in x of h(x).

h((2x + 5)^2)

expanding value using the formula (a+b)^2=a^2+2ab+b^2

h(4x^2+20x+25)

Thirdly, substituting the value of h(x) in x of h(x).

-2(4x^2+20x+25)

opening bracket

-8x^2-40x-50

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