Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 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 — 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.f(x) = x + 6 and g(x) = −4x + 2. Find g(f(x)) in simplest form.
Answer: −4x − 22
- g(f(x)) = −4(x + 6) + 2
- = −4x − 22
2.If f(x) = −2x2 − 3x − 1, find f(0).
Answer: −1
- Replace x with 0: −2(0)2 − 3(0) − 1
- = −1
3.If f(x) = 3x2 − 4x + 4, find f(3).
Answer: 19
- Replace x with 3: 3(3)2 − 4(3) + 4
- = 19
4.f(x) = −3x and g(x) = −3x − 3. Find f(g(x)) in simplest form.
Answer: 9x + 9
- f(g(x)) = −3(−3x − 3)
- = 9x + 9
5.f(x) = −4x + 1 and g(x) = −x. Find g(f(x)) in simplest form.
Answer: 4x − 1
- g(f(x)) = −1(−4x + 1)
- = 4x − 1
6.f(x) = 4x + 1 and g(x) = −3x. Find g(f(x)) in simplest form.
Answer: −12x − 3
- g(f(x)) = −3(4x + 1)
- = −12x − 3
7.If f(x) = −2x2 − 2x − 2, find f(4).
Answer: −42
- Replace x with 4: −2(4)2 − 2(4) − 2
- = −42
8.f(x) = 2x and g(x) = 2x − 4. Find f(g(x)) in simplest form.
Answer: 4x − 8
- f(g(x)) = 2(2x − 4)
- = 4x − 8
9.f(x) = −4x − 6 and g(x) = 3x + 2. Find g(f(x)) in simplest form.
Answer: −12x − 16
- g(f(x)) = 3(−4x − 6) + 2
- = −12x − 16
10.If f(x) = 3x2 + 2x − 6, find f(−3).
Answer: 15
- Replace x with −3: 3(−3)2 + 2(−3) − 6
- = 15
11.f(x) = −2x − 6 and g(x) = 3x + 6. Find f(g(x)) in simplest form.
Answer: −6x − 18
- f(g(x)) = −2(3x + 6) − 6
- = −6x − 18
12.f(x) = 2x − 2 and g(x) = −4x − 2. Find f(g(x)) in simplest form.
Answer: −8x − 6
- f(g(x)) = 2(−4x − 2) − 2
- = −8x − 6
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.