Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 3 — 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 3 — 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) = 3x2 + 4x − 6, find f(2).
Answer: 14
- Replace x with 2: 3(2)2 + 4(2) − 6
- = 14
2.f(x) = −4x + 5 and g(x) = −2x + 1. Find g(f(x)) in simplest form.
Answer: 8x − 9
- g(f(x)) = −2(−4x + 5) + 1
- = 8x − 9
3.f(x) = −4x − 1 and g(x) = −4x − 1. Find f(g(x)) in simplest form.
Answer: 16x + 3
- f(g(x)) = −4(−4x − 1) − 1
- = 16x + 3
4.If f(x) = x2 + 6x − 9, find f(3).
Answer: 18
- Replace x with 3: (3)2 + 6(3) − 9
- = 18
5.f(x) = 2x − 6 and g(x) = −4x − 2. Find g(f(x)) in simplest form.
Answer: −8x + 22
- g(f(x)) = −4(2x − 6) − 2
- = −8x + 22
6.If f(x) = 2x2 − 7, find f(5).
Answer: 43
- Replace x with 5: 2(5)2 − 7
- = 43
7.If f(x) = −3x2 − 3x − 5, find f(0).
Answer: −5
- Replace x with 0: −3(0)2 − 3(0) − 5
- = −5
8.If f(x) = −2x2 + 5x − 4, find f(5).
Answer: −29
- Replace x with 5: −2(5)2 + 5(5) − 4
- = −29
9.If f(x) = 4x2 + x + 1, find f(4).
Answer: 69
- Replace x with 4: 4(4)2 + (4) + 1
- = 69
10.If f(x) = 2x2 + 3x − 1, find f(1).
Answer: 4
- Replace x with 1: 2(1)2 + 3(1) − 1
- = 4
11.f(x) = −2x + 6 and g(x) = 5x + 2. Find f(g(x)) in simplest form.
Answer: −10x + 2
- f(g(x)) = −2(5x + 2) + 6
- = −10x + 2
12.f(x) = 5x and g(x) = −3x − 1. Find g(f(x)) in simplest form.
Answer: −15x − 1
- g(f(x)) = −3(5x) − 1
- = −15x − 1
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