Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · FunctionsYear 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — 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) = −x + 4 and g(x) = −x + 3. Find g(f(x)) in simplest form.
Answer: x − 1
- g(f(x)) = −1(−x + 4) + 3
- = x − 1
2.If f(x) = −2x2 − 5x + 4, find f(−3).
Answer: 1
- Replace x with −3: −2(−3)2 − 5(−3) + 4
- = 1
3.f(x) = −4x − 6 and g(x) = −2x − 4. Find g(f(x)) in simplest form.
Answer: 8x + 8
- g(f(x)) = −2(−4x − 6) − 4
- = 8x + 8
4.If f(x) = 2x2 + 3x + 4, find f(−1).
Answer: 3
- Replace x with −1: 2(−1)2 + 3(−1) + 4
- = 3
5.If f(x) = 4x2 − 4x − 1, find f(1).
Answer: −1
- Replace x with 1: 4(1)2 − 4(1) − 1
- = −1
6.f(x) = 3x − 4 and g(x) = 5x − 3. Find f(g(x)) in simplest form.
Answer: 15x − 13
- f(g(x)) = 3(5x − 3) − 4
- = 15x − 13
7.f(x) = x − 2 and g(x) = 4x − 4. Find f(g(x)) in simplest form.
Answer: 4x − 6
- f(g(x)) = 1(4x − 4) − 2
- = 4x − 6
8.If f(x) = 3x2 − 5x + 7, find f(−2).
Answer: 29
- Replace x with −2: 3(−2)2 − 5(−2) + 7
- = 29
9.If f(x) = 2x2 + 4x + 9, find f(2).
Answer: 25
- Replace x with 2: 2(2)2 + 4(2) + 9
- = 25
10.If f(x) = 3x2 − 5x − 6, find f(2).
Answer: −4
- Replace x with 2: 3(2)2 − 5(2) − 6
- = −4
11.f(x) = x + 4 and g(x) = −x + 1. Find f(g(x)) in simplest form.
Answer: −x + 5
- f(g(x)) = 1(−x + 1) + 4
- = −x + 5
12.If f(x) = x2 − 6x − 1, find f(2).
Answer: −9
- Replace x with 2: (2)2 − 6(2) − 1
- = −9
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