Answer:
(g - h)(-4x) = 4x - 2
Step-by-step explanation:
This problem is one dealing with "composite functions." We are given the definitions of functions g(x) and h(x) and are asked to find the difference between g and h, namely, what is left if we subtact h from g. After having done that, we replace x in this composite function with the input (-4x).
The difference (g - h)(x) is as follows: g(x) - h(x) = -x + 4x - [4x + 2].
If we simplify the algebra, we get g(x) - h(x) = -x + 4x - [4x + 2] = -x - 2.
Next, substitute -4x for x in this last result. We get (g - h)(-4x) = 4x - 2.
Please note: You might want to check out your g(x) = -x + 4x. Normally we would write this as +3x.
