10th Grade Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 10th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Functions10th Grade 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.If f(x) = −x2 + 6x − 6, find f(−3).
Answer: −33
- Replace x with −3: −(−3)2 + 6(−3) − 6
- = −33
2.f(x) = −x + 4 and g(x) = 2x − 4. Find g(f(x)) in simplest form.
Answer: −2x + 4
- g(f(x)) = 2(−x + 4) − 4
- = −2x + 4
3.If f(x) = 2x2 − 9, find f(1).
Answer: −7
- Replace x with 1: 2(1)2 − 9
- = −7
4.If f(x) = −2x2 + 5x + 8, find f(1).
Answer: 11
- Replace x with 1: −2(1)2 + 5(1) + 8
- = 11
5.If f(x) = 3x2 + 6x − 9, find f(2).
Answer: 15
- Replace x with 2: 3(2)2 + 6(2) − 9
- = 15
6.f(x) = −2x + 6 and g(x) = −2x − 2. Find f(g(x)) in simplest form.
Answer: 4x + 10
- f(g(x)) = −2(−2x − 2) + 6
- = 4x + 10
7.If f(x) = 4x2 − 3x + 2, find f(−2).
Answer: 24
- Replace x with −2: 4(−2)2 − 3(−2) + 2
- = 24
8.If f(x) = −x2 − 3x − 6, find f(−4).
Answer: −10
- Replace x with −4: −(−4)2 − 3(−4) − 6
- = −10
9.If f(x) = x2 + 6x + 2, find f(3).
Answer: 29
- Replace x with 3: (3)2 + 6(3) + 2
- = 29
10.If f(x) = −2x2 + 4x + 2, find f(−2).
Answer: −14
- Replace x with −2: −2(−2)2 + 4(−2) + 2
- = −14
11.f(x) = 2x − 3 and g(x) = 5x − 5. Find g(f(x)) in simplest form.
Answer: 10x − 20
- g(f(x)) = 5(2x − 3) − 5
- = 10x − 20
12.If f(x) = 4x2 − 4x + 1, find f(1).
Answer: 1
- Replace x with 1: 4(1)2 − 4(1) + 1
- = 1
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: