Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — 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 3 — 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.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 =
2.Find the inverse function of f(x) = −2x − 1.
Answer: f−1(x) =
- y = −2x − 1
- Swap x and y: x = −2y − 1
- Solve for y: y =
3.f(x) = 3x + 2 and g(x) = −x. Find f(g(x)) in simplest form.
Answer: −3x + 2
- f(g(x)) = 3(−x) + 2
- = −3x + 2
4.Find the inverse function of f(x) = −5x − 2.
Answer: f−1(x) =
- y = −5x − 2
- Swap x and y: x = −5y − 2
- Solve for y: y =
5.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 =
6.f(x) = −4x + 4 and g(x) = 2x − 3. Find f(g(x)) in simplest form.
Answer: −8x + 16
- f(g(x)) = −4(2x − 3) + 4
- = −8x + 16
7.f(x) = −x − 5 and g(x) = −4x + 4. Find g(f(x)) in simplest form.
Answer: 4x + 24
- g(f(x)) = −4(−x − 5) + 4
- = 4x + 24
8.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 =
9.f(x) = 4x + 4 and g(x) = 5x − 1. Find g(f(x)) in simplest form.
Answer: 20x + 19
- g(f(x)) = 5(4x + 4) − 1
- = 20x + 19
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) = −3x − 5 and g(x) = x − 2. Find g(f(x)) in simplest form.
Answer: −3x − 7
- g(f(x)) = 1(−3x − 5) − 2
- = −3x − 7
12.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 =
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