Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — 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 2 — 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) = 3x + 8.
Answer: f−1(x) =
- y = 3x + 8
- Swap x and y: x = 3y + 8
- Solve for y: y =
2.f(x) = 2x − 2 and g(x) = −4x − 1. Find f(g(x)) in simplest form.
Answer: −8x − 4
- f(g(x)) = 2(−4x − 1) − 2
- = −8x − 4
3.f(x) = x − 6 and g(x) = 4x + 2. Find g(f(x)) in simplest form.
Answer: 4x − 22
- g(f(x)) = 4(x − 6) + 2
- = 4x − 22
4.Find the inverse function of f(x) = 6x + 7.
Answer: f−1(x) =
- y = 6x + 7
- Swap x and y: x = 6y + 7
- Solve for y: y =
5.f(x) = 3x − 1 and g(x) = −x − 1. Find f(g(x)) in simplest form.
Answer: −3x − 4
- f(g(x)) = 3(−x − 1) − 1
- = −3x − 4
6.f(x) = −3x + 1 and g(x) = −x − 4. Find g(f(x)) in simplest form.
Answer: 3x − 5
- g(f(x)) = −1(−3x + 1) − 4
- = 3x − 5
7.Find the inverse function of f(x) = −6x − 7.
Answer: f−1(x) =
- y = −6x − 7
- Swap x and y: x = −6y − 7
- Solve for y: y =
8.f(x) = 5x − 4 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: 5x + 21
- f(g(x)) = 5(x + 5) − 4
- = 5x + 21
9.f(x) = −x + 6 and g(x) = 5x + 5. Find f(g(x)) in simplest form.
Answer: −5x + 1
- f(g(x)) = −1(5x + 5) + 6
- = −5x + 1
10.f(x) = 4x − 2 and g(x) = 3x + 2. Find g(f(x)) in simplest form.
Answer: 12x − 4
- g(f(x)) = 3(4x − 2) + 2
- = 12x − 4
11.f(x) = −4x + 1 and g(x) = −4x − 2. Find f(g(x)) in simplest form.
Answer: 16x + 9
- f(g(x)) = −4(−4x − 2) + 1
- = 16x + 9
12.Find the inverse function of f(x) = 5x − 3.
Answer: f−1(x) =
- y = 5x − 3
- Swap x and y: x = 5y − 3
- Solve for y: y =
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.