Study Guide
Functions, Domain and Range
A senior study guide to function notation, the vertical line test, and finding the domain and range of common functions. Worked examples…
- Difficulty
- Level 2 · Standard
- Time
- 25 min
Extra practice for Year 12 Function Notation, Composites and Inverses Worksheet — Level 3: the same skill with fresh questions.
WorksheetYear 12Level 3 · Challenge
Free Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4
Practice Set 4 for Year 12 Function Notation, Composites and Inverses Worksheet — Level 3: the same skill and level with a fresh set of questions and a full answer sheet.
More practice: Set 1 · Practice Set 2 · Practice Set 3 — same skill, fresh questions, full answers.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 12
- Subject
- Maths
- Topic
- Functions
- Difficulty
- Level 3 · Challenge
- Estimated time
- 15 minutes
- Curriculum
- New Zealand Curriculum
- Questions
- 12
- Answers
- Included, with working
- Format
- PDF (A4), print or complete online
Students will practise
- evaluating functions in f(x) notation
- forming composite functions
- finding inverse functions
Curriculum: New Zealand Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4
How to use this worksheet
- Print the PDF or complete it on screen. Write the student's name and date at the top.
- Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
- Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
- Record the score, celebrate what went well, then follow the "What's next" suggestion.
Common questions
Who is this worksheet for?
Year 12 students (typically ages 16–17) working on functions. It is pitched at level 3 · challenge; an easier version is linked above.
Are the answers included?
Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.
How long does it take?
About 15 minutes for 12 questions. Short, regular sessions work best: two or three a week beats one long one.
Do I need to sign up to download?
No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.
What should we do next?
Try Year 12 Differentiation (Power Rule) Worksheet — Level 1.
Preview
Success TutoringWorksheetsYear 12 · Mathematics · FunctionsYear 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4
Name
Date
Score /
f(x) notation means "the value of the function at x". For a composite, substitute the inner function into the outer one. For an inverse, swap x and y and solve for y.
1.Find the inverse function of f(x) = x − 4.
2.Find the inverse function of f(x) = 5x + 5.
3.f(x) = 3x + 1 and g(x) = 4x + 5. Find f(g(x)) in simplest form.
4.f(x) = x − 5 and g(x) = 3x + 5. Find g(f(x)) in simplest form.
5.Find the inverse function of f(x) = 2x + 2.
6.f(x) = 5x − 4 and g(x) = −3x + 2. Find g(f(x)) in simplest form.
7.Find the inverse function of f(x) = x + 5.
8.Find the inverse function of f(x) = 5x − 8.
9.f(x) = −x + 3 and g(x) = −2x − 4. Find f(g(x)) in simplest form.
10.f(x) = 3x and g(x) = −2x + 2. Find f(g(x)) in simplest form.
11.f(x) = −x + 4 and g(x) = 2x − 5. Find f(g(x)) in simplest form.
12.f(x) = 5x + 4 and g(x) = −3x. Find g(f(x)) in simplest form.
Preview — the PDF contains the full resource and answer sheet.
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Evaluate functions written in f(x) notation, form composite functions and find the inverse of a linear function. Builds confidence with…
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- 12 questions
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Year 12 Function Notation, Composites and Inverses Worksheet — Level 2
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- Time
- 15 min
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- Answers
- Answers included
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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3
Evaluate functions written in f(x) notation, form composite functions and find the inverse of a linear function. A challenge set for…
- Difficulty
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- Time
- 15 min
- Questions
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- Answers
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Functions in other year levels
- Year 11 Function Notation, Composites and Inverses Worksheet — Level 1
Worksheet · Year 11 · Functions · Level 1 · Easier
- Year 11 Function Notation, Composites and Inverses Worksheet — Level 2
Worksheet · Year 11 · Functions · Level 2 · Standard
- Year 13 Function Notation, Composites and Inverses Worksheet — Level 1
Worksheet · Year 13 · Functions · Level 1 · Easier
- Year 13 Function Notation, Composites and Inverses Worksheet — Level 2
Worksheet · Year 13 · Functions · Level 2 · Standard
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About this resource
- Created by
- Success Tutoring Maths Team
- Reviewed by
- Success Tutoring
- Last reviewed
- 1 October 2026
- How it was made
- Generated by checked procedures
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