Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 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.If f(x) = −x2 − 5x − 5, find f(1).
Answer: −11
- Replace x with 1: −(1)2 − 5(1) − 5
- = −11
2.f(x) = 4x + 2 and g(x) = −x. Find g(f(x)) in simplest form.
Answer: −4x − 2
- g(f(x)) = −1(4x + 2)
- = −4x − 2
3.If f(x) = x2 − 4x − 4, find f(4).
Answer: −4
- Replace x with 4: (4)2 − 4(4) − 4
- = −4
4.f(x) = 3x + 3 and g(x) = −x − 2. Find f(g(x)) in simplest form.
Answer: −3x − 3
- f(g(x)) = 3(−x − 2) + 3
- = −3x − 3
5.If f(x) = −3x2 + 2, find f(0).
Answer: 2
- Replace x with 0: −3(0)2 + 2
- = 2
6.If f(x) = −2x2 − 2x + 5, find f(3).
Answer: −19
- Replace x with 3: −2(3)2 − 2(3) + 5
- = −19
7.If f(x) = x2 − 5x − 5, find f(4).
Answer: −9
- Replace x with 4: (4)2 − 5(4) − 5
- = −9
8.f(x) = 3x + 1 and g(x) = 3x + 1. Find g(f(x)) in simplest form.
Answer: 9x + 4
- g(f(x)) = 3(3x + 1) + 1
- = 9x + 4
9.If f(x) = −3x2 − x + 8, find f(−2).
Answer: −2
- Replace x with −2: −3(−2)2 − (−2) + 8
- = −2
10.If f(x) = −2x2 − 6x + 8, find f(4).
Answer: −48
- Replace x with 4: −2(4)2 − 6(4) + 8
- = −48
11.f(x) = −4x − 4 and g(x) = −x + 5. Find g(f(x)) in simplest form.
Answer: 4x + 9
- g(f(x)) = −1(−4x − 4) + 5
- = 4x + 9
12.If f(x) = 4x2 − 6x − 6, find f(−4).
Answer: 82
- Replace x with −4: 4(−4)2 − 6(−4) − 6
- = 82
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