Form 4 & 5 Unit 1 Lesson 3 – Composite Functions

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 g(x) function as the value of x in the f(x) function.

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 becomes the main function. We then substitute f(x) function as the value of x in g(x).

  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