Year 11 Function Notation, Composites and Inverses Worksheet — Level 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 — 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) = 4x2 + 3x − 4, find f(4).
Answer: 72
- Replace x with 4: 4(4)2 + 3(4) − 4
- = 72
2.If f(x) = −x2 − 4x − 3, find f(−1).
Answer: 0
- Replace x with −1: −(−1)2 − 4(−1) − 3
- = 0
3.If f(x) = 2x2 − x − 8, find f(4).
Answer: 20
- Replace x with 4: 2(4)2 − (4) − 8
- = 20
4.If f(x) = 3x2 + x − 6, find f(−4).
Answer: 38
- Replace x with −4: 3(−4)2 + (−4) − 6
- = 38
5.f(x) = 3x − 4 and g(x) = 3x − 6. Find f(g(x)) in simplest form.
Answer: 9x − 22
- f(g(x)) = 3(3x − 6) − 4
- = 9x − 22
6.f(x) = −x + 1 and g(x) = 4x − 3. Find f(g(x)) in simplest form.
Answer: −4x + 4
- f(g(x)) = −1(4x − 3) + 1
- = −4x + 4
7.f(x) = 4x − 1 and g(x) = −4x − 4. Find g(f(x)) in simplest form.
Answer: −16x
- g(f(x)) = −4(4x − 1) − 4
- = −16x
8.f(x) = x − 3 and g(x) = 5x + 1. Find f(g(x)) in simplest form.
Answer: 5x − 2
- f(g(x)) = 1(5x + 1) − 3
- = 5x − 2
9.f(x) = 2x + 3 and g(x) = −3x − 4. Find f(g(x)) in simplest form.
Answer: −6x − 5
- f(g(x)) = 2(−3x − 4) + 3
- = −6x − 5
10.If f(x) = 2x2 + 5x + 5, find f(−1).
Answer: 2
- Replace x with −1: 2(−1)2 + 5(−1) + 5
- = 2
11.If f(x) = 4x2 − 5x + 1, find f(−3).
Answer: 52
- Replace x with −3: 4(−3)2 − 5(−3) + 1
- = 52
12.f(x) = 4x + 4 and g(x) = −2x + 5. Find g(f(x)) in simplest form.
Answer: −8x − 3
- g(f(x)) = −2(4x + 4) + 5
- = −8x − 3
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