Question

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

Answer 1

You want h(h) = h. That is,

3h+4 = h
3(3x+4) + 4 = 3x+4
9x + 12 + 4 = 3x + 4
6x = -12
x = -2

h(-2) = 3(-2) + 4 = -2

Or, using h^-1, you could say, recalling that
h^-1(h(x)) = x

So, h^-1(h(h)) = h^-1(h)
h = x
3x+4 = x
2x = -4
x = -2