Free Grade 3 Introducing Inverse Functions Common Errors Lessons
Free Grade 3 lessons for Introducing Inverse Functions Common Errors: 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing inverse functions common errors
Explain introducing inverse functions common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing inverse functions common errors
Calculate introducing inverse functions common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing inverse functions common errors
Compare introducing inverse functions common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing inverse functions common errors
Justify introducing inverse functions common errors 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 Inverse Functions Common Errors 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) = 5x − 3. Find f(2).[1]
- 2.f(x) = 4x + 6. Find f(-1).[1]
- 3.f(x) = 5x + 6. Find f(0).[1]
- 4.f(x) = 2x + 5. Find f(5).[1]
- 5.f(x) = 3x − 2. Find f(0).[2]
- 6.f(x) = 6x + 2. Find f(-2).[2]
- 7.f(x) = 4x − 6. Find f(0).[2]
- 8.f(x) = 4x − 5. Find f(2).[2]
- 9.f(x) = 3x + 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x − 4. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x + 0. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 5x − 7. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 7
Replace x with 2: 5 × 2 − 3. = 7
2. 2
Replace x with -1: 4 × (-1) + 6. = 2
3. 6
Replace x with 0: 5 × 0 + 6. = 6
4. 15
Replace x with 5: 2 × 5 + 5. = 15
5. -2
Replace x with 0: 3 × 0 − 2. = -2
6. -10
Replace x with -2: 6 × (-2) + 2. = -10
7. -6
Replace x with 0: 4 × 0 − 6. = -6
8. 3
Replace x with 2: 4 × 2 − 5. = 3
9. f⁻¹(x) = (x − 2) / 3
Write y = 3x + 2 and swap x and y. Rearrange for y: y = (x − 2) / 3.
10. f⁻¹(x) = (x + 4) / 2
Write y = 2x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 2.
11. f⁻¹(x) = (x − 0) / 4
Write y = 4x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 4.
12. f⁻¹(x) = (x + 7) / 5
Write y = 5x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 5.
Worked examples
f(x) = 6x + 1. Find f(2).
- Replace x with 2: 6 × 2 + 1.
- = 13
- Answer: 13
f(x) = 6x − 7. Find f(4).
- Replace x with 4: 6 × 4 − 7.
- = 17
- Answer: 17
f(x) = 2x + 8. Find the inverse f⁻¹(x).
- Write y = 2x + 8 and swap x and y.
- Rearrange for y: y = (x − 8) / 2.
- Answer: f⁻¹(x) = (x − 8) / 2
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.
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Frequently asked
- Is this Grade 3 Introducing Inverse Functions Common Errors lesson really free?
- Yes. Every lessons 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 Introducing Inverse Functions Word Problems, Introducing Inverse Functions Techniques, Composite Functions. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Inverse Functions Common Errors?
- Move on to Working with Inverse Functions, Inverse Functions in Context, which build directly on this idea.
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