Check two functions for the inverse property:

Compare f(g(x)) and g(f(x)), where f(x) = 3x + 4 and g(x) = 2x - 5.

f(g(x)) = f(2x - 5) = 3(2x - 5) + 4 = 6x - 11

g(f(x)) = g(3x + 4) = 2(3x + 4) - 5 = 6x + 3

These don't agree with the inverse function properties, and are not inverses of each other.

Compare f(x) = 5x - 1 and g(x) = (x + 1)/5 in the same way:

Since we get back to x in each case, these are inverses of each other.

Test Problem: Are the following inverses of each other? f(x) = 2x + 7 and g(x) = (x-3)/2