CIE IGCSE Maths

Revision Notes

2.12.2 Compound Functions

What is a compound function?

  • A compound function is one function applied to the output of another function

What do compound functions look like?

  • The notation you will see is:
    fg(x)
  • it can be written as:
    f(g(x))
    and means “f applied to the output of g(x)” – ie. g(x) happens FIRST !

How does a compound function work?

  • If you are putting a number into fg(x):
  1. Put the number into g(x)
  2. Put the output into f(x)
    eg. if f(x) = 2x + 1 and g(x) = 1/x
    then fg(2) = f(½) =2 × ½ + 1 = 2
    and gf(2) = g(2 × 2 + 1) = g(5) = 1/5
  • If you are using algebra:
  1. For fg(x) put g(x) wherever you see x in f(x)
  2. Substitute g(x) with the right hand side of g(x)=…
  3. SIMPLIFY if necessary
    eg. if f(x) = 2x + 1 and g(x) = 1 / x
    then fg(x) = f(1/x) = 2 × 1 / x + 1 = 2 / x +1
    and gf(x) = g(2 × x + 1) = g(2x + 1) = 1 / 2x+1

Exam Tip

Make sure you are applying the functions in the correct order.

The letter nearest the bracket is the function applied first.

Worked Example

Compound Functions Worked Example, downloadable IGCSE & GCSE Maths revision notes

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