Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 13 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · FunctionsYear 13 Function Notation, Composites and Inverses Worksheet — Level 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.f(x) = −2x − 4 and g(x) = 4x + 2. Find g(f(x)) in simplest form.
Answer: −8x − 14
- g(f(x)) = 4(−2x − 4) + 2
- = −8x − 14
2.Find the inverse function of f(x) = −6x − 6.
Answer: f−1(x) =
- y = −6x − 6
- Swap x and y: x = −6y − 6
- Solve for y: y =
3.Find the inverse function of f(x) = −6x − 2.
Answer: f−1(x) =
- y = −6x − 2
- Swap x and y: x = −6y − 2
- Solve for y: y =
4.Find the inverse function of f(x) = −6x − 9.
Answer: f−1(x) =
- y = −6x − 9
- Swap x and y: x = −6y − 9
- Solve for y: y =
5.f(x) = x − 3 and g(x) = x. Find g(f(x)) in simplest form.
Answer: x − 3
- g(f(x)) = 1(x − 3)
- = x − 3
6.Find the inverse function of f(x) = −2x.
Answer: f−1(x) = −
- y = −2x
- Swap x and y: x = −2y
- Solve for y: y = −
7.Find the inverse function of f(x) = −x − 5.
Answer: f−1(x) = −x − 5
- y = −x − 5
- Swap x and y: x = −y − 5
- Solve for y: y = −x − 5
8.Find the inverse function of f(x) = −2x + 6.
Answer: f−1(x) =
- y = −2x + 6
- Swap x and y: x = −2y + 6
- Solve for y: y =
9.f(x) = 2x + 4 and g(x) = −2x + 1. Find f(g(x)) in simplest form.
Answer: −4x + 6
- f(g(x)) = 2(−2x + 1) + 4
- = −4x + 6
10.Find the inverse function of f(x) = −3x + 8.
Answer: f−1(x) =
- y = −3x + 8
- Swap x and y: x = −3y + 8
- Solve for y: y =
11.f(x) = 4x − 4 and g(x) = −4x − 2. Find g(f(x)) in simplest form.
Answer: −16x + 14
- g(f(x)) = −4(4x − 4) − 2
- = −16x + 14
12.Find the inverse function of f(x) = x + 7.
Answer: f−1(x) = x − 7
- y = x + 7
- Swap x and y: x = y + 7
- Solve for y: y = x − 7
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