Question

Let g(x) = -2x + 8 and h(x) = 3x + 4. For what value of x is composition (g o h)(x) = (h o g)(x). If no such value exists, type in DNE in the space provided.

Answer 1

Calculate the two separate functions (g o h)(x) and (h o g)(x).

Some textbooks would write them as
g{f(x)] and f{g(x)}

g{f(x)} = -2(3x+4)+8 = -6 x
f{g(x)} = 3(-2x+8) +4 = -6 x +28

Then set them equal and solve for x.
DNE in this case.