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) = −4x + 5 and g(x) = 5x + 3. Find g(f(x)) in simplest form.
Answer: −20x + 28
- g(f(x)) = 5(−4x + 5) + 3
- = −20x + 28
2.f(x) = 3x − 4 and g(x) = −4x − 6. Find g(f(x)) in simplest form.
Answer: −12x + 10
- g(f(x)) = −4(3x − 4) − 6
- = −12x + 10
3.Find the inverse function of f(x) = −2x − 4.
Answer: f−1(x) =
- y = −2x − 4
- Swap x and y: x = −2y − 4
- Solve for y: y =
4.f(x) = −2x − 2 and g(x) = 3x + 3. Find g(f(x)) in simplest form.
Answer: −6x − 3
- g(f(x)) = 3(−2x − 2) + 3
- = −6x − 3
5.f(x) = 4x + 2 and g(x) = 5x + 1. Find f(g(x)) in simplest form.
Answer: 20x + 6
- f(g(x)) = 4(5x + 1) + 2
- = 20x + 6
6.f(x) = −2x + 6 and g(x) = −3x − 6. Find g(f(x)) in simplest form.
Answer: 6x − 24
- g(f(x)) = −3(−2x + 6) − 6
- = 6x − 24
7.f(x) = −4x − 4 and g(x) = −x − 5. Find g(f(x)) in simplest form.
Answer: 4x − 1
- g(f(x)) = −1(−4x − 4) − 5
- = 4x − 1
8.Find the inverse function of f(x) = 4x − 1.
Answer: f−1(x) =
- y = 4x − 1
- Swap x and y: x = 4y − 1
- Solve for y: y =
9.f(x) = −x + 1 and g(x) = x + 1. Find f(g(x)) in simplest form.
Answer: −x
- f(g(x)) = −1(x + 1) + 1
- = −x
10.Find the inverse function of f(x) = 3x + 3.
Answer: f−1(x) =
- y = 3x + 3
- Swap x and y: x = 3y + 3
- Solve for y: y =
11.f(x) = x and g(x) = −x + 1. Find g(f(x)) in simplest form.
Answer: −x + 1
- g(f(x)) = −1(x) + 1
- = −x + 1
12.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 =
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.