Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 2 — Practice Set 3 — 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) = 2x2 − 4, find f(2).
Answer: 4
- Replace x with 2: 2(2)2 − 4
- = 4
2.If f(x) = −3x2 − 3x + 1, find f(−1).
Answer: 1
- Replace x with −1: −3(−1)2 − 3(−1) + 1
- = 1
3.If f(x) = x2 − 4x − 1, find f(0).
Answer: −1
- Replace x with 0: (0)2 − 4(0) − 1
- = −1
4.If f(x) = 2x2 + 5x + 1, find f(−4).
Answer: 13
- Replace x with −4: 2(−4)2 + 5(−4) + 1
- = 13
5.f(x) = 4x + 1 and g(x) = 2x. Find f(g(x)) in simplest form.
Answer: 8x + 1
- f(g(x)) = 4(2x) + 1
- = 8x + 1
6.f(x) = −3x + 6 and g(x) = 4x + 1. Find g(f(x)) in simplest form.
Answer: −12x + 25
- g(f(x)) = 4(−3x + 6) + 1
- = −12x + 25
7.If f(x) = 4x2 + x + 1, find f(−1).
Answer: 4
- Replace x with −1: 4(−1)2 + (−1) + 1
- = 4
8.f(x) = −x + 2 and g(x) = x − 3. Find f(g(x)) in simplest form.
Answer: −x + 5
- f(g(x)) = −1(x − 3) + 2
- = −x + 5
9.If f(x) = 4x2 − 8, find f(5).
Answer: 92
- Replace x with 5: 4(5)2 − 8
- = 92
10.f(x) = 4x − 3 and g(x) = −x + 4. Find f(g(x)) in simplest form.
Answer: −4x + 13
- f(g(x)) = 4(−x + 4) − 3
- = −4x + 13
11.If f(x) = −2x2 + 3x − 1, find f(2).
Answer: −3
- Replace x with 2: −2(2)2 + 3(2) − 1
- = −3
12.If f(x) = −3x2 + 1, find f(−3).
Answer: −26
- Replace x with −3: −3(−3)2 + 1
- = −26
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: