f(x) = x² and g(x) = x + 3. Find fg(x) in simplest form.
Step 1 Identify the order
fg(x) means do g first, then f
So we need f(g(x))
Step 2 Substitute g(x) into f
g(x) = x + 3
f(g(x)) = f(x + 3) = (x + 3)²
Step 3 Expand and simplify
fg(x) = (x + 3)²
= x² + 6x + 9
fg(x) = x² + 6x + 9
This study notes covers Worked Example 2: Composite Function Expressions within Composite Functions for GCSE Mathematics. Revise Composite Functions in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Composite Functions
The composite function fg(x) means: A) Apply g first, then apply f to the result B) Apply f first, then apply g to the result C) Multiply f(x) by g(x) D) Add f(x) to g(x)
Explain why, in general, fg(x) and gf(x) are NOT equal. You may use an example to support your explanation.