What is the equation for h(f(x))?

Question

Given f(x) = x / (4-4x) and h(x) = x^2 + 4x What is the equation for h(f(x))?

Answer 1

h(f(x)) = [x / (4 - 4x)]^2 + 4[x / (4 - 4x)]

Answer 2

this is easy, wherever you see x in h(x), put in x/(4-4x)

so you get ((x/(4-4x)))^2 + 4(x/(4-4x))

Answer 3

h(x) = x^2 + 4x

h(f) = f^2 + 4f

we know that f = x / (4 - 4x)

so h(f(x)) = [x / (4 - 4x)]^2 + 4[x / (4 - 4x)]

h(f(x)) = [x / (4(1 - x))]^2 + 4x / [4(1 - x)]

h(f(x)) = x^2 / [16(1 - x)^2] + x / (1 - x)

h(f(x)) = x^2 / [16(1 - x)^2) + 16x(1 - x) / [16(1 - x)^2]

h(f(x) = (x^2 + 16x - 16x^2) / [16(1 - x)^2]

h(f(x) = (16x - 15x^2) / [16(1 - x)^2]

Answer 4

(-15x^2 + 16x)/(4-4x)^2

what the Boom Shaka said is the original equation, mine is in simplest form.