Year 13 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 13 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · FunctionsYear 13 Function Notation, Composites and Inverses Worksheet — Level 2 — 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.If f(x) = 3x2 − 6x − 1, find f(−4).
Answer: 71
- Replace x with −4: 3(−4)2 − 6(−4) − 1
- = 71
2.f(x) = 4x + 1 and g(x) = 3x + 5. Find g(f(x)) in simplest form.
Answer: 12x + 8
- g(f(x)) = 3(4x + 1) + 5
- = 12x + 8
3.If f(x) = −2x2 + 4x + 1, find f(3).
Answer: −5
- Replace x with 3: −2(3)2 + 4(3) + 1
- = −5
4.f(x) = 2x + 4 and g(x) = −x + 1. Find g(f(x)) in simplest form.
Answer: −2x − 3
- g(f(x)) = −1(2x + 4) + 1
- = −2x − 3
5.f(x) = 4x − 4 and g(x) = 3x − 4. Find f(g(x)) in simplest form.
Answer: 12x − 20
- f(g(x)) = 4(3x − 4) − 4
- = 12x − 20
6.If f(x) = 3x2 + 5x + 5, find f(−1).
Answer: 3
- Replace x with −1: 3(−1)2 + 5(−1) + 5
- = 3
7.f(x) = −2x − 3 and g(x) = x − 2. Find f(g(x)) in simplest form.
Answer: −2x + 1
- f(g(x)) = −2(x − 2) − 3
- = −2x + 1
8.If f(x) = −x2 − 4x + 6, find f(1).
Answer: 1
- Replace x with 1: −(1)2 − 4(1) + 6
- = 1
9.If f(x) = −3x2 + 6x + 2, find f(−3).
Answer: −43
- Replace x with −3: −3(−3)2 + 6(−3) + 2
- = −43
10.If f(x) = −2x2 − x − 5, find f(1).
Answer: −8
- Replace x with 1: −2(1)2 − (1) − 5
- = −8
11.f(x) = 2x − 5 and g(x) = 4x + 6. Find g(f(x)) in simplest form.
Answer: 8x − 14
- g(f(x)) = 4(2x − 5) + 6
- = 8x − 14
12.If f(x) = 3x2 + 4x − 9, find f(−2).
Answer: −5
- Replace x with −2: 3(−2)2 + 4(−2) − 9
- = −5
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.
Great work. Here's what to try next: