Composite Functions

Functions can be chained, for example $gf(5)$, these are called composite functions.

Example

Example functions: $f(x) = 7x - 3$ and $g(x) = 3x + 8$. Given these examples, $gf(3)$ would equal $62$.

$$\begin{align} f(3) & = 7(3) - 3 \\ & = 21 = 3 \\ & = 18 \\ \\ g(18) & = 3(18) + 8 \\ & = 54 + 8 \\ & = 62 \\ \end{align}$$

Algebraic Example

Using the previously given example functions, you could work out a function for $gf(x)$.

$$\begin{align} gf(x) & = 3(7x - 3) + 8 \\ & = 21x - 9 + 8 \\ & = 21x -1 \end{align}$$

Given that $gf(x) = 21x - 7$, you can work out $gf(3)$ using a single function.

$$\begin{align} gf(x) & = 21(3) - 1 \\ & = 63 -1 \\ & = 62 \end{align}$$

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