Input Equals Output

Let g(x) and f(x) be functions.
Choose a value of x and input it into g(x).
Take the output of g(x) and input it into f(x).
Compare the input of g(x) to the output of f(x).

For example, let g(x) = 3x+2, and f(x) = 4x – 8.
Choose x = 2 to input into g(x) and the output will be g(2)= 3(2) + 2 = 8.
Now input 8 into f(x) and get an output of f(8) = 4(8) – 8 = 24.
So the number we started with is 2, and the number we ended with is 24.

Find two functions (besides f(x) = x and g(x) = x) so that the input of g(x) is always equal to the output of f(x).
How many pairs can you find?