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.f(x) = 4x + 3 and g(x) = x + 2. Find f(g(x)) in simplest form.
Answer: 4x + 11
- f(g(x)) = 4(x + 2) + 3
- = 4x + 11
2.If f(x) = x2 + 2x + 7, find f(2).
Answer: 15
- Replace x with 2: (2)2 + 2(2) + 7
- = 15
3.If f(x) = −3x2 + x − 9, find f(5).
Answer: −79
- Replace x with 5: −3(5)2 + (5) − 9
- = −79
4.f(x) = x − 1 and g(x) = 2x + 1. Find f(g(x)) in simplest form.
Answer: 2x
- f(g(x)) = 1(2x + 1) − 1
- = 2x
5.If f(x) = −x2 + 5, find f(−2).
Answer: 1
- Replace x with −2: −(−2)2 + 5
- = 1
6.If f(x) = −3x2 − 2x + 2, find f(5).
Answer: −83
- Replace x with 5: −3(5)2 − 2(5) + 2
- = −83
7.f(x) = −x and g(x) = −4x + 5. Find f(g(x)) in simplest form.
Answer: 4x − 5
- f(g(x)) = −1(−4x + 5)
- = 4x − 5
8.f(x) = −2x − 6 and g(x) = x + 1. Find f(g(x)) in simplest form.
Answer: −2x − 8
- f(g(x)) = −2(x + 1) − 6
- = −2x − 8
9.If f(x) = −3x2, find f(2).
Answer: −12
- Replace x with 2: −3(2)2
- = −12
10.If f(x) = −3x2 + 5x − 2, find f(3).
Answer: −14
- Replace x with 3: −3(3)2 + 5(3) − 2
- = −14
11.If f(x) = 2x2 − 4x + 8, find f(1).
Answer: 6
- Replace x with 1: 2(1)2 − 4(1) + 8
- = 6
12.If f(x) = 2x2 + 2x − 2, find f(2).
Answer: 10
- Replace x with 2: 2(2)2 + 2(2) − 2
- = 10
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