Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 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 — 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.f(x) = −2x − 2 and g(x) = −3x + 4. Find f(g(x)) in simplest form.
Answer: 6x − 10
- f(g(x)) = −2(−3x + 4) − 2
- = 6x − 10
2.If f(x) = 2x2 + 4x + 9, find f(1).
Answer: 15
- Replace x with 1: 2(1)2 + 4(1) + 9
- = 15
3.If f(x) = 4x2 − 5x − 4, find f(−1).
Answer: 5
- Replace x with −1: 4(−1)2 − 5(−1) − 4
- = 5
4.If f(x) = −x2 − 3x − 4, find f(1).
Answer: −8
- Replace x with 1: −(1)2 − 3(1) − 4
- = −8
5.f(x) = −3x and g(x) = −2x + 3. Find f(g(x)) in simplest form.
Answer: 6x − 9
- f(g(x)) = −3(−2x + 3)
- = 6x − 9
6.f(x) = −x − 2 and g(x) = −2x + 1. Find g(f(x)) in simplest form.
Answer: 2x + 5
- g(f(x)) = −2(−x − 2) + 1
- = 2x + 5
7.If f(x) = −2x2 − x − 9, find f(−2).
Answer: −15
- Replace x with −2: −2(−2)2 − (−2) − 9
- = −15
8.f(x) = −x + 5 and g(x) = 3x − 6. Find f(g(x)) in simplest form.
Answer: −3x + 11
- f(g(x)) = −1(3x − 6) + 5
- = −3x + 11
9.f(x) = −4x + 2 and g(x) = −x − 5. Find f(g(x)) in simplest form.
Answer: 4x + 22
- f(g(x)) = −4(−x − 5) + 2
- = 4x + 22
10.If f(x) = 3x2 − x + 5, find f(2).
Answer: 15
- Replace x with 2: 3(2)2 − (2) + 5
- = 15
11.f(x) = −4x − 2 and g(x) = −2x + 6. Find g(f(x)) in simplest form.
Answer: 8x + 10
- g(f(x)) = −2(−4x − 2) + 6
- = 8x + 10
12.If f(x) = −x2 − 5x + 5, find f(−2).
Answer: 11
- Replace x with −2: −(−2)2 − 5(−2) + 5
- = 11
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