Composites: A Function of a Function

Previously, we have been substituting numbers, expressions and variables other than x into a function.

You can also substitute a function within a function, hence combining two functions into one. For instance, the statement f(g(x)) would mean to replace x with the function g(x).

For example, if f(x) = 3x+1 and g(x) = 5x², then f(g(x)) would be:

f(g(x)) = 3•(g(x)) + 1
            = 3•(5x²) + 1
            = 15x² + 1

Note: The notation (f ° g)(x) or f[g(x)] is equivalent to f(g(x)).