What is a composite function?

A composite function is one where the input to the function is another function.

When one writes f(x), f is the output and x is a place-holder for some input; we say that the function f, is evaluated at x.

The placeholder x could be replaced with:

1) a number, 2 say: f(2)

2) another letter, q say: f(q)

3) a function or expression, g(x) = 3x - 2

f(3x - 2) or equivalently f(g(x)), sometimes written as fg(x)

---- Please note, fg(x) is NOT f multiplied by g(x). ----

So, if f(x) = 2x + 7, then

f(2) = 2(2) + 7 = 4 + 7 = 11

f(q) = 2q + 7

fg(x) = f(3x - 2) = 2(3x - 2) + 7

= 6x - 4 + 7

= 6x + 3

A composite function is created when one function is substituted in another function.