Question

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

h(g(f(x)))

Answer 1

Hello here is a solution :
h(g(f(x))) ?

g(f(x))= g(2x+5)=(2x+5)²=(2x)²+2(2x)(5)+5² = 4x²+20x+25
h(g(f(x)))(x) = h(4x²+20x+25) = -2(4x²+20x+25)
h(g(f(x)))(x) = -8x²-40x-50

Answer 2

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

Explanation:

`f(x) = 2x + 5`

`g(x)=x^2`

`h(x)=-2x`

`h(g(f(x)))`, first replace f(x) with 2x+5

`h(g(2x+5))`

Replace 2x+5 for x in g(x).
`g(2x+5)=(2x+5)^2= (2x+5)(2x+5)= 4x^2+20x+25`

`h(g(2x+5))` becomes
`h(4x^2+20x+25)`

Replace x with 4x^2+20x+25 in h(x)

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