Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — 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 3 — Practice Set 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.Find the inverse function of f(x) = 2x + 8.
Answer: f−1(x) =
- y = 2x + 8
- Swap x and y: x = 2y + 8
- Solve for y: y =
2.Find the inverse function of f(x) = 4x + 7.
Answer: f−1(x) =
- y = 4x + 7
- Swap x and y: x = 4y + 7
- Solve for y: y =
3.Find the inverse function of f(x) = 2x − 9.
Answer: f−1(x) =
- y = 2x − 9
- Swap x and y: x = 2y − 9
- Solve for y: y =
4.Find the inverse function of f(x) = −3x + 2.
Answer: f−1(x) =
- y = −3x + 2
- Swap x and y: x = −3y + 2
- Solve for y: y =
5.Find the inverse function of f(x) = x + 6.
Answer: f−1(x) = x − 6
- y = x + 6
- Swap x and y: x = y + 6
- Solve for y: y = x − 6
6.Find the inverse function of f(x) = 3x − 1.
Answer: f−1(x) =
- y = 3x − 1
- Swap x and y: x = 3y − 1
- Solve for y: y =
7.f(x) = −2x + 3 and g(x) = 3x + 2. Find f(g(x)) in simplest form.
Answer: −6x − 1
- f(g(x)) = −2(3x + 2) + 3
- = −6x − 1
8.f(x) = 3x + 3 and g(x) = x − 6. Find f(g(x)) in simplest form.
Answer: 3x − 15
- f(g(x)) = 3(x − 6) + 3
- = 3x − 15
9.Find the inverse function of f(x) = 3x − 9.
Answer: f−1(x) =
- y = 3x − 9
- Swap x and y: x = 3y − 9
- Solve for y: y =
10.Find the inverse function of f(x) = 2x + 5.
Answer: f−1(x) =
- y = 2x + 5
- Swap x and y: x = 2y + 5
- Solve for y: y =
11.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
12.Find the inverse function of f(x) = −2x + 3.
Answer: f−1(x) =
- y = −2x + 3
- Swap x and y: x = −2y + 3
- Solve for y: y =
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