10th Grade Function Notation, Composites and Inverses Worksheet — Level 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 — 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) = 5x + 5 and g(x) = −x. Find f(g(x)) in simplest form.
Answer: −5x + 5
- f(g(x)) = 5(−x) + 5
- = −5x + 5
2.If f(x) = −2x2 + 2x − 3, find f(0).
Answer: −3
- Replace x with 0: −2(0)2 + 2(0) − 3
- = −3
3.If f(x) = −x2 + 4x, find f(5).
Answer: −5
- Replace x with 5: −(5)2 + 4(5)
- = −5
4.If f(x) = x2 − 2x + 1, find f(−2).
Answer: 9
- Replace x with −2: (−2)2 − 2(−2) + 1
- = 9
5.f(x) = −4x − 1 and g(x) = −3x − 1. Find f(g(x)) in simplest form.
Answer: 12x + 3
- f(g(x)) = −4(−3x − 1) − 1
- = 12x + 3
6.If f(x) = x2 + 4x + 1, find f(−3).
Answer: −2
- Replace x with −3: (−3)2 + 4(−3) + 1
- = −2
7.If f(x) = −2x2 − 5x + 6, find f(−4).
Answer: −6
- Replace x with −4: −2(−4)2 − 5(−4) + 6
- = −6
8.f(x) = −4x + 3 and g(x) = −4x − 4. Find f(g(x)) in simplest form.
Answer: 16x + 19
- f(g(x)) = −4(−4x − 4) + 3
- = 16x + 19
9.If f(x) = −x2 − 2x − 1, find f(−3).
Answer: −4
- Replace x with −3: −(−3)2 − 2(−3) − 1
- = −4
10.f(x) = 4x + 6 and g(x) = 2x − 6. Find g(f(x)) in simplest form.
Answer: 8x + 6
- g(f(x)) = 2(4x + 6) − 6
- = 8x + 6
11.f(x) = −4x + 4 and g(x) = 4x. Find g(f(x)) in simplest form.
Answer: −16x + 16
- g(f(x)) = 4(−4x + 4)
- = −16x + 16
12.If f(x) = 2x2 + 6x + 8, find f(2).
Answer: 28
- Replace x with 2: 2(2)2 + 6(2) + 8
- = 28
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: