AlgebraStudy Notes

Worked Example 2: Composite Function Expressions

Part of Composite Functions — GCSE Mathematics

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 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 7

Practice

14 questions

Recall

12 flashcards

Worked Example 2: Composite Function Expressions

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

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)

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)

1 markfoundation

Explain why, in general, fg(x) and gf(x) are NOT equal. You may use an example to support your explanation.

2 marksfoundation

Worked Example 2: Composite Function Expressions

Worked Example 2: Composite Function Expressions

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Practice Questions for Composite Functions

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