Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · FunctionsYear 11 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.f(x) = −x + 3 and g(x) = x − 6. Find f(g(x)) in simplest form.
Answer: −x + 9
- f(g(x)) = −1(x − 6) + 3
- = −x + 9
2.f(x) = −3x + 2 and g(x) = 5x + 1. Find f(g(x)) in simplest form.
Answer: −15x − 1
- f(g(x)) = −3(5x + 1) + 2
- = −15x − 1
3.f(x) = 3x − 2 and g(x) = 4x + 3. Find f(g(x)) in simplest form.
Answer: 12x + 7
- f(g(x)) = 3(4x + 3) − 2
- = 12x + 7
4.Find the inverse function of f(x) = 5x + 6.
Answer: f−1(x) =
- y = 5x + 6
- Swap x and y: x = 5y + 6
- Solve for y: y =
5.Find the inverse function of f(x) = −3x + 5.
Answer: f−1(x) =
- y = −3x + 5
- Swap x and y: x = −3y + 5
- Solve for y: y =
6.f(x) = 4x + 6 and g(x) = −4x − 4. Find f(g(x)) in simplest form.
Answer: −16x − 10
- f(g(x)) = 4(−4x − 4) + 6
- = −16x − 10
7.Find the inverse function of f(x) = −3x + 4.
Answer: f−1(x) =
- y = −3x + 4
- Swap x and y: x = −3y + 4
- Solve for y: y =
8.Find the inverse function of f(x) = 4x + 6.
Answer: f−1(x) =
- y = 4x + 6
- Swap x and y: x = 4y + 6
- Solve for y: y =
9.f(x) = −x − 5 and g(x) = 5x + 3. Find f(g(x)) in simplest form.
Answer: −5x − 8
- f(g(x)) = −1(5x + 3) − 5
- = −5x − 8
10.f(x) = 2x − 3 and g(x) = 2x − 5. Find f(g(x)) in simplest form.
Answer: 4x − 13
- f(g(x)) = 2(2x − 5) − 3
- = 4x − 13
11.f(x) = −2x − 6 and g(x) = 4x + 3. Find f(g(x)) in simplest form.
Answer: −8x − 12
- f(g(x)) = −2(4x + 3) − 6
- = −8x − 12
12.Find the inverse function of f(x) = 6x − 5.
Answer: f−1(x) =
- y = 6x − 5
- Swap x and y: x = 6y − 5
- 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.