AlgebraStudy Notes

Worked Example 3: Showing Order Matters

Part of Composite Functions — GCSE Mathematics

This study notes covers Worked Example 3: Showing Order Matters 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 6 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 6 of 7

Practice

14 questions

Recall

12 flashcards

Worked Example 3: Showing Order Matters

f(x) = 2x and g(x) = x + 1. Find fg(x) and gf(x). Are they the same?

Step 1 Find fg(x)

fg(x) = f(g(x)) = f(x + 1)

= 2(x + 1) = 2x + 2

Step 2 Find gf(x)

gf(x) = g(f(x)) = g(2x)

= 2x + 1

Step 3 Compare

fg(x) = 2x + 2

gf(x) = 2x + 1

They are NOT the same!

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 3: Showing Order Matters

Worked Example 3: Showing Order Matters

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Practice Questions for Composite Functions

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