For this case we have the following functions:
[tex]f (x) = 2x + 5\\g (x) = x ^ 2\\h (x) = - 2x[/tex]
So, we have to by definition:
[tex]g (f (x)) = (2x + 5) ^ 2 = (2x) ^ 2 + 2 (2x) (5) + 5 ^ 2 = 4x ^ 2 + 20x + 25[/tex]
So:[tex]h (g (f (x))) = - 2 (4x ^ 2 + 20x + 25) = - 8x ^ 2-40x-50[/tex]
We take common factor:
[tex]- (8x ^ 2 + 40x + 50)[/tex]
Answer:
[tex]h (g (f (x))) = - (8x ^ 2 + 40x + 50)[/tex]
