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) = −4x and g(x) = −3x + 1. Find f(g(x)) in simplest form.
Answer: 12x − 4
- f(g(x)) = −4(−3x + 1)
- = 12x − 4
2.If f(x) = 2x2 + 4x + 7, find f(−4).
Answer: 23
- Replace x with −4: 2(−4)2 + 4(−4) + 7
- = 23
3.If f(x) = −x2 − x + 4, find f(−3).
Answer: −2
- Replace x with −3: −(−3)2 − (−3) + 4
- = −2
4.f(x) = 3x − 6 and g(x) = x − 2. Find g(f(x)) in simplest form.
Answer: 3x − 8
- g(f(x)) = 1(3x − 6) − 2
- = 3x − 8
5.If f(x) = 2x2 − 2x − 6, find f(5).
Answer: 34
- Replace x with 5: 2(5)2 − 2(5) − 6
- = 34
6.If f(x) = −2x2 − 2x − 5, find f(−2).
Answer: −9
- Replace x with −2: −2(−2)2 − 2(−2) − 5
- = −9
7.f(x) = −3x − 4 and g(x) = 4x − 4. Find f(g(x)) in simplest form.
Answer: −12x + 8
- f(g(x)) = −3(4x − 4) − 4
- = −12x + 8
8.f(x) = x − 3 and g(x) = 4x + 2. Find g(f(x)) in simplest form.
Answer: 4x − 10
- g(f(x)) = 4(x − 3) + 2
- = 4x − 10
9.f(x) = 2x + 3 and g(x) = 5x − 4. Find g(f(x)) in simplest form.
Answer: 10x + 11
- g(f(x)) = 5(2x + 3) − 4
- = 10x + 11
10.f(x) = 2x + 4 and g(x) = −4x + 6. Find g(f(x)) in simplest form.
Answer: −8x − 10
- g(f(x)) = −4(2x + 4) + 6
- = −8x − 10
11.If f(x) = 3x2 − 2x − 2, find f(−1).
Answer: 3
- Replace x with −1: 3(−1)2 − 2(−1) − 2
- = 3
12.If f(x) = x2 + 2x + 6, find f(0).
Answer: 6
- Replace x with 0: (0)2 + 2(0) + 6
- = 6
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