Question

How do you find g[h(x)] and h[g(x)] given `h(x)=2x-1` `g(x)=3x+4`?

Answer 1

g(h(x))=6x +1 and h(g(x)) = 6x+7

Explanation:

Basically , this is a substitution exercise.

g(h(x)) = g(2x-1) . Now substitute x = 2x-1 in for x in g(x)

hence g(2x-1) = 3(2x-1)+4 = 6x - 3 + 4 = 6x + 1

Similarly : h(g(x)) = h(3x+4) substitute x = 3x+4 in h(x)

hence h(3x+4) = 2(3x + 4 ) - 1 = 6x + 8 - 1 = 6x + 7