__Objective__

At the end of the lesson, students should be able to

- Form composite functions as defined by
**gf(x) = g(f(x)).**

Composite functions deal with more than one function.

__Example 1 __

If **f(x)** = 3x and **g(x)** = x – 1 then we can find ** fg **(x).

The first letter ** f** becomes the main function. We then substitute the

**f[g(x)]** = 3(x – 1) since g(x)= x – 1

= 3x – 3

We can similarly find the composite function ** gf(x**). The first letter

** g [f(x)]** = (3x) – 1 since f(x)= 3x

= 3x – 1

__Example 2__

If f(x) = 5x + 4 and g(x) = x – 1, find **fg(x)** and **gf(x).**

__Solution__

f(x) = 5x + 4 g(x) = x – 1

fg(x) = 5(x – 1) + 4

= 5x – 5 + 4

= 5x – 1

**fg(x) = 5x – 1**

gf(x) = (5x + 4) – 1

= 5x + 3

**gf(x) = 5x + 3**

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