proving inverses

Question

how would you prove these two equations are or are not inverses of each other?

F(x) = ½ x + 5

G(x) = 2x - 10

Answer 1

By definition, for one-to-one inverses, F(G(x)) = G(F(x)) = x. If this test fails, then the functions are not inverses of each of each other.

For example:

F(G(x)) = (2x-10)/2 +5 = x-5+5 = x.

G(F(x)) = 2(x/2+5) -10 = x + 10 - 10 = x.

So these functions are inverses of each other.