A **composite function** are two or more functions combined together. The output from one function is used as the input for the other.

If there are two functions f(*x*) and g(*x*), and the output from g(*x*) is to be used as the input for f(*x*), then the composite function is f(g(*x*)). It is more normally written simply as fg(*x*).

Work from the innermost function out; for fg(*x*), evaluate the function g(*x*) first, then f(*x*) using the answer from g(*x*). Order is important: fg(*x*) is different to gf(*x*).

If `f(x) = x^2` and `g(x) = 2x - 4`, evaluate `fg(5)`.

Work out `g(5)` first: 2 x 5 - 4 = 6

This is the input to `f(x)`: `f(6) = 6^2 = 36`

Answer: 36

Write `fg(x)`, in terms of `x`, when `f(x) = 3x - 4` and `g(x) = 4 - 3x`.

Substitute the output from `g(x)` into `f(x)`:

`fg(x) = 3(g(x)) - 4`

`= 3(4 - 3x) - 4`

`= 12 - 9x - 4`

`= 8 - 9x`

Answer: ` 8 - 9x`

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