Free Grade 3 Introducing Composite Functions Worksheets
Free Grade 3 worksheets for Introducing Composite Functions: 12 real questions with a full answer key and worked solutions. A function is a rule that turns an input into an output. The inverse function reverses it.
Free
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing composite functions
Explain introducing composite functions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing composite functions
Calculate introducing composite functions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing composite functions
Compare introducing composite functions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing composite functions
Justify introducing composite functions accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Composite Functions works
A function is a rule that turns an input into an output. The inverse function reverses it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.f(x) = 2x − 5. Find f(5).[1]
- 2.f(x) = 6x − 4. Find f(-1).[1]
- 3.f(x) = 5x − 2. Find f(1).[1]
- 4.f(x) = 2x + 5. Find f(-3).[1]
- 5.f(x) = 2x − 2. Find f(-3).[2]
- 6.f(x) = 5x − 7. Find f(2).[2]
- 7.f(x) = 3x + 3. Find f(-4).[2]
- 8.f(x) = 3x − 5. Find f(3).[2]
- 9.f(x) = 5x − 6. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 4x − 7. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 5x − 3. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 2. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 5
Replace x with 5: 2 × 5 − 5. = 5
2. -10
Replace x with -1: 6 × (-1) − 4. = -10
3. 3
Replace x with 1: 5 × 1 − 2. = 3
4. -1
Replace x with -3: 2 × (-3) + 5. = -1
5. -8
Replace x with -3: 2 × (-3) − 2. = -8
6. 3
Replace x with 2: 5 × 2 − 7. = 3
7. -9
Replace x with -4: 3 × (-4) + 3. = -9
8. 4
Replace x with 3: 3 × 3 − 5. = 4
9. f⁻¹(x) = (x + 6) / 5
Write y = 5x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 5.
10. f⁻¹(x) = (x + 7) / 4
Write y = 4x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 4.
11. f⁻¹(x) = (x + 3) / 5
Write y = 5x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 5.
12. f⁻¹(x) = (x + 2) / 3
Write y = 3x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 3.
Worked examples
f(x) = 6x + 2. Find f(0).
- Replace x with 0: 6 × 0 + 2.
- = 2
- Answer: 2
f(x) = 2x − 5. Find f(-2).
- Replace x with -2: 2 × (-2) − 5.
- = -9
- Answer: -9
f(x) = 3x − 7. Find the inverse f⁻¹(x).
- Write y = 3x − 7 and swap x and y.
- Rearrange for y: y = (x + 7) / 3.
- Answer: f⁻¹(x) = (x + 7) / 3
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads f(3) as f × 3.
Correction: f(3) means 'put 3 into the rule'.
Reverses operations in the wrong order for the inverse.
Correction: Undo the last step first.
Teacher tips
- · Use function machines before notation.
Parent tips
- · Play 'guess my rule' with numbers.
Real-life applications
- · Converting temperatures, phone-plan costs.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Introducing Composite Functions
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Frequently asked
- Is this Grade 3 Introducing Composite Functions worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Domain and Range. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Composite Functions?
- Move on to Working with Composite Functions, Composite Functions in Context, Function Notation, Domain and Range, which build directly on this idea.
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