Question

G(x)=-x + 4x h(x)=4x + 2 Find (g-h)(-4x) How do I answer this question

Answer 1

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.