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 + 4x − 8, find f(−4).
Answer: 8
- Replace x with −4: 2(−4)2 + 4(−4) − 8
- = 8
2.f(x) = −3x + 4 and g(x) = −3x + 4. Find g(f(x)) in simplest form.
Answer: 9x − 8
- g(f(x)) = −3(−3x + 4) + 4
- = 9x − 8
3.f(x) = 2x and g(x) = x + 6. Find f(g(x)) in simplest form.
Answer: 2x + 12
- f(g(x)) = 2(x + 6)
- = 2x + 12
4.f(x) = 3x + 3 and g(x) = 5x. Find f(g(x)) in simplest form.
Answer: 15x + 3
- f(g(x)) = 3(5x) + 3
- = 15x + 3
5.f(x) = 3x + 6 and g(x) = 3x + 4. Find f(g(x)) in simplest form.
Answer: 9x + 18
- f(g(x)) = 3(3x + 4) + 6
- = 9x + 18
6.If f(x) = −x2 − 6x − 7, find f(2).
Answer: −23
- Replace x with 2: −(2)2 − 6(2) − 7
- = −23
7.If f(x) = 2x2 + 2x + 9, find f(−1).
Answer: 9
- Replace x with −1: 2(−1)2 + 2(−1) + 9
- = 9
8.If f(x) = −2x2 − 2x + 8, find f(2).
Answer: −4
- Replace x with 2: −2(2)2 − 2(2) + 8
- = −4
9.f(x) = −x + 2 and g(x) = 2x − 2. Find f(g(x)) in simplest form.
Answer: −2x + 4
- f(g(x)) = −1(2x − 2) + 2
- = −2x + 4
10.f(x) = 5x + 1 and g(x) = −x + 3. Find g(f(x)) in simplest form.
Answer: −5x + 2
- g(f(x)) = −1(5x + 1) + 3
- = −5x + 2
11.f(x) = 3x − 2 and g(x) = x − 6. Find g(f(x)) in simplest form.
Answer: 3x − 8
- g(f(x)) = 1(3x − 2) − 6
- = 3x − 8
12.f(x) = −2x − 6 and g(x) = x − 6. Find g(f(x)) in simplest form.
Answer: −2x − 12
- g(f(x)) = 1(−2x − 6) − 6
- = −2x − 12
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.