****college algebra****
posted by Brianna on .
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.

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