Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 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.f(x) = −4x + 6 and g(x) = −3x − 3. Find g(f(x)) in simplest form.
Answer: 12x − 21
- g(f(x)) = −3(−4x + 6) − 3
- = 12x − 21
2.If f(x) = −2x2 − 5x − 2, find f(−4).
Answer: −14
- Replace x with −4: −2(−4)2 − 5(−4) − 2
- = −14
3.If f(x) = 2x2 − 7, find f(0).
Answer: −7
- Replace x with 0: 2(0)2 − 7
- = −7
4.f(x) = 5x − 4 and g(x) = 4x − 6. Find g(f(x)) in simplest form.
Answer: 20x − 22
- g(f(x)) = 4(5x − 4) − 6
- = 20x − 22
5.If f(x) = 2x2 + 5x − 8, find f(1).
Answer: −1
- Replace x with 1: 2(1)2 + 5(1) − 8
- = −1
6.If f(x) = 3x2 − 6x + 1, find f(−3).
Answer: 46
- Replace x with −3: 3(−3)2 − 6(−3) + 1
- = 46
7.If f(x) = −3x2 + 4x + 3, find f(2).
Answer: −1
- Replace x with 2: −3(2)2 + 4(2) + 3
- = −1
8.f(x) = −3x − 3 and g(x) = −3x − 5. Find f(g(x)) in simplest form.
Answer: 9x + 12
- f(g(x)) = −3(−3x − 5) − 3
- = 9x + 12
9.If f(x) = 2x2 − x − 7, find f(3).
Answer: 8
- Replace x with 3: 2(3)2 − (3) − 7
- = 8
10.f(x) = x + 1 and g(x) = −2x − 4. Find f(g(x)) in simplest form.
Answer: −2x − 3
- f(g(x)) = 1(−2x − 4) + 1
- = −2x − 3
11.If f(x) = 4x2 + 4, find f(0).
Answer: 4
- Replace x with 0: 4(0)2 + 4
- = 4
12.If f(x) = −3x2 + 2x + 9, find f(5).
Answer: −56
- Replace x with 5: −3(5)2 + 2(5) + 9
- = −56
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: