Question

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

h(g(f(x))) = ___ x²+ ___ x + ___

Answer 1

-8

-40

-50

Explanation:

Answer 2

For this case we have the following functions:

`f (x) = 2x + 5\\g (x) = x ^ 2\\h (x) = - 2x`

So, we have to by definition:

`g (f (x)) = (2x + 5) ^ 2 = (2x) ^ 2 + 2 (2x) (5) + 5 ^ 2 = 4x ^ 2 + 20x + 25`

So:
`h (g (f (x))) = - 2 (4x ^ 2 + 20x + 25) = - 8x ^ 2-40x-50`

We take common factor:

`- (8x ^ 2 + 40x + 50)`

Answer:

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