Year 10 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 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.f(x) = 5x − 2 and g(x) = −4x + 6. Find g(f(x)) in simplest form.
Answer: −20x + 14
- g(f(x)) = −4(5x − 2) + 6
- = −20x + 14
2.f(x) = 5x + 4 and g(x) = 5x + 5. Find f(g(x)) in simplest form.
Answer: 25x + 29
- f(g(x)) = 5(5x + 5) + 4
- = 25x + 29
3.Find the inverse function of f(x) = −2x − 7.
Answer: f−1(x) =
- y = −2x − 7
- Swap x and y: x = −2y − 7
- Solve for y: y =
4.f(x) = −4x + 1 and g(x) = 2x + 5. Find g(f(x)) in simplest form.
Answer: −8x + 7
- g(f(x)) = 2(−4x + 1) + 5
- = −8x + 7
5.Find the inverse function of f(x) = 4x − 7.
Answer: f−1(x) =
- y = 4x − 7
- Swap x and y: x = 4y − 7
- Solve for y: y =
6.Find the inverse function of f(x) = −6x + 8.
Answer: f−1(x) =
- y = −6x + 8
- Swap x and y: x = −6y + 8
- Solve for y: y =
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) = 2x + 6 and g(x) = x + 1. Find f(g(x)) in simplest form.
Answer: 2x + 8
- f(g(x)) = 2(x + 1) + 6
- = 2x + 8
9.Find the inverse function of f(x) = 6x + 6.
Answer: f−1(x) =
- y = 6x + 6
- Swap x and y: x = 6y + 6
- Solve for y: y =
10.f(x) = 5x − 6 and g(x) = −2x − 6. Find f(g(x)) in simplest form.
Answer: −10x − 36
- f(g(x)) = 5(−2x − 6) − 6
- = −10x − 36
11.f(x) = −3x + 1 and g(x) = 3x + 2. Find f(g(x)) in simplest form.
Answer: −9x − 5
- f(g(x)) = −3(3x + 2) + 1
- = −9x − 5
12.Find the inverse function of f(x) = −x − 9.
Answer: f−1(x) = −x − 9
- y = −x − 9
- Swap x and y: x = −y − 9
- Solve for y: y = −x − 9
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.