AlgebraDeep Dive

Method: Finding Composite Functions

Part of Composite Functions — GCSE Mathematics

This deep dive covers Method: Finding Composite Functions 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 3 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 7

Practice

14 questions

Recall

12 flashcards

Method: Finding Composite Functions

1Identify which function to do first (inner function)

2Substitute the first function into the second

3Simplify the expression

4Check your answer by substituting values

Keep building this topic

Read this section alongside the surrounding pages in Composite Functions. That gives you the full topic sequence instead of a single isolated revision point.

Key Facts Worked Example 1: Composite Functions with Values Chaining Functions Together Worked Example 2: Composite Function Expressions

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

Quick Recall Flashcards

What does fg(x) mean?

fg(x) = f(g(x)): apply g first (inner function), then apply f to the result. Do the function closest to x first.

What is a composite function?

A function formed by chaining two functions together. The output of one function becomes the input of the next.

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Key Facts

Worked Example 1: Composite Functions with Values