Year 11 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 2 — 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 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) = −x + 3 and g(x) = 4x − 6. Find g(f(x)) in simplest form.
Answer: −4x + 6
- g(f(x)) = 4(−x + 3) − 6
- = −4x + 6
2.If f(x) = 3x2 − 6x + 3, find f(−4).
Answer: 75
- Replace x with −4: 3(−4)2 − 6(−4) + 3
- = 75
3.f(x) = −4x + 2 and g(x) = 4x − 3. Find f(g(x)) in simplest form.
Answer: −16x + 14
- f(g(x)) = −4(4x − 3) + 2
- = −16x + 14
4.If f(x) = 2x2 − 6x − 9, find f(−1).
Answer: −1
- Replace x with −1: 2(−1)2 − 6(−1) − 9
- = −1
5.f(x) = x + 2 and g(x) = −x − 1. Find g(f(x)) in simplest form.
Answer: −x − 3
- g(f(x)) = −1(x + 2) − 1
- = −x − 3
6.If f(x) = 3x2 + 7, find f(0).
Answer: 7
- Replace x with 0: 3(0)2 + 7
- = 7
7.If f(x) = −2x2 + 3, find f(3).
Answer: −15
- Replace x with 3: −2(3)2 + 3
- = −15
8.If f(x) = 2x2 + 6x − 6, find f(−3).
Answer: −6
- Replace x with −3: 2(−3)2 + 6(−3) − 6
- = −6
9.If f(x) = 2x2 + x − 5, find f(−1).
Answer: −4
- Replace x with −1: 2(−1)2 + (−1) − 5
- = −4
10.If f(x) = 3x2 − 2x − 9, find f(−2).
Answer: 7
- Replace x with −2: 3(−2)2 − 2(−2) − 9
- = 7
11.If f(x) = 3x2 + 5x + 6, find f(−1).
Answer: 4
- Replace x with −1: 3(−1)2 + 5(−1) + 6
- = 4
12.f(x) = 5x + 5 and g(x) = −3x − 3. Find g(f(x)) in simplest form.
Answer: −15x − 18
- g(f(x)) = −3(5x + 5) − 3
- = −15x − 18
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