Composite Functions

A composite function is the combination of two separate functions operating one after another. Two composite functions containing one independent variable x can be written f(g(x)), pronounced "f of g of x". The second outer function operates on the output of the first function. So the internal function is calculated first and the external function processes the results produced by the inner function. The output of the second function is the range set of the composite function and the input for the first function is the domain of the composite function. The output of the first function's range is used as the input for the domain of the second function in a composite function.

Composite functions:
If y = g(x) is y = 2x + 1,
2 times x plus 1,
and y = f(x) is y = x²,
y = x squared,
then y = f(g(x)) is y = (2x + 1)²,
(2 times x plus 1) squared.