Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers
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) = −4x + 8.
Answer: f−1(x) =
- y = −4x + 8
- Swap x and y: x = −4y + 8
- Solve for y: y =
2.Find the inverse function of f(x) = 7x + 1.
Answer: f−1(x) =
- y = 7x + 1
- Swap x and y: x = 7y + 1
- Solve for y: y =
3.f(x) = −3x + 3 and g(x) = −3x + 5. Find g(f(x)) in simplest form.
Answer: 9x − 4
- g(f(x)) = −3(−3x + 3) + 5
- = 9x − 4
4.Find the inverse function of f(x) = −6x − 9.
Answer: f−1(x) =
- y = −6x − 9
- Swap x and y: x = −6y − 9
- Solve for y: y =
5.Find the inverse function of f(x) = 5x + 9.
Answer: f−1(x) =
- y = 5x + 9
- Swap x and y: x = 5y + 9
- Solve for y: y =
6.Find the inverse function of f(x) = 2x − 5.
Answer: f−1(x) =
- y = 2x − 5
- Swap x and y: x = 2y − 5
- Solve for y: y =
7.f(x) = x − 5 and g(x) = −4x − 6. Find g(f(x)) in simplest form.
Answer: −4x + 14
- g(f(x)) = −4(x − 5) − 6
- = −4x + 14
8.Find the inverse function of f(x) = −x + 1.
Answer: f−1(x) = −x + 1
- y = −x + 1
- Swap x and y: x = −y + 1
- Solve for y: y = −x + 1
9.f(x) = −3x − 1 and g(x) = 3x. Find g(f(x)) in simplest form.
Answer: −9x − 3
- g(f(x)) = 3(−3x − 1)
- = −9x − 3
10.Find the inverse function of f(x) = −4x + 5.
Answer: f−1(x) =
- y = −4x + 5
- Swap x and y: x = −4y + 5
- Solve for y: y =
11.Find the inverse function of f(x) = 2x − 3.
Answer: f−1(x) =
- y = 2x − 3
- Swap x and y: x = 2y − 3
- Solve for y: y =
12.f(x) = 3x + 2 and g(x) = −4x + 3. Find f(g(x)) in simplest form.
Answer: −12x + 11
- f(g(x)) = 3(−4x + 3) + 2
- = −12x + 11
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.