Year 11 Function Notation, Composites and Inverses Worksheet — Level 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 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 + 9, find f(3).
Answer: −36
- Replace x with 3: −3(3)2 − 6(3) + 9
- = −36
2.If f(x) = 3x2 − 3x + 3, find f(−2).
Answer: 21
- Replace x with −2: 3(−2)2 − 3(−2) + 3
- = 21
3.f(x) = 2x − 4 and g(x) = −x + 2. Find g(f(x)) in simplest form.
Answer: −2x + 6
- g(f(x)) = −1(2x − 4) + 2
- = −2x + 6
4.f(x) = 2x − 2 and g(x) = −2x. Find g(f(x)) in simplest form.
Answer: −4x + 4
- g(f(x)) = −2(2x − 2)
- = −4x + 4
5.If f(x) = −x2 + x − 5, find f(2).
Answer: −7
- Replace x with 2: −(2)2 + (2) − 5
- = −7
6.If f(x) = −2x2 + x + 7, find f(1).
Answer: 6
- Replace x with 1: −2(1)2 + (1) + 7
- = 6
7.f(x) = −x − 5 and g(x) = 3x − 4. Find g(f(x)) in simplest form.
Answer: −3x − 19
- g(f(x)) = 3(−x − 5) − 4
- = −3x − 19
8.If f(x) = 2x2 + x + 3, find f(−2).
Answer: 9
- Replace x with −2: 2(−2)2 + (−2) + 3
- = 9
9.f(x) = −3x + 6 and g(x) = x + 1. Find g(f(x)) in simplest form.
Answer: −3x + 7
- g(f(x)) = 1(−3x + 6) + 1
- = −3x + 7
10.f(x) = x − 1 and g(x) = 2x − 2. Find f(g(x)) in simplest form.
Answer: 2x − 3
- f(g(x)) = 1(2x − 2) − 1
- = 2x − 3
11.f(x) = 4x + 6 and g(x) = −3x + 5. Find f(g(x)) in simplest form.
Answer: −12x + 26
- f(g(x)) = 4(−3x + 5) + 6
- = −12x + 26
12.f(x) = x + 5 and g(x) = −x − 5. Find f(g(x)) in simplest form.
Answer: −x
- f(g(x)) = 1(−x − 5) + 5
- = −x
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.