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) = −5x − 5.
Answer: f−1(x) =
- y = −5x − 5
- Swap x and y: x = −5y − 5
- Solve for y: y =
2.f(x) = −2x + 3 and g(x) = −x + 5. Find g(f(x)) in simplest form.
Answer: 2x + 2
- g(f(x)) = −1(−2x + 3) + 5
- = 2x + 2
3.f(x) = −x + 2 and g(x) = −3x + 4. Find g(f(x)) in simplest form.
Answer: 3x − 2
- g(f(x)) = −3(−x + 2) + 4
- = 3x − 2
4.Find the inverse function of f(x) = −5x + 3.
Answer: f−1(x) =
- y = −5x + 3
- Swap x and y: x = −5y + 3
- Solve for y: y =
5.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 =
6.f(x) = −4x − 4 and g(x) = 2x + 1. Find f(g(x)) in simplest form.
Answer: −8x − 8
- f(g(x)) = −4(2x + 1) − 4
- = −8x − 8
7.f(x) = 5x − 5 and g(x) = 3x − 2. Find g(f(x)) in simplest form.
Answer: 15x − 17
- g(f(x)) = 3(5x − 5) − 2
- = 15x − 17
8.f(x) = 5x + 6 and g(x) = −3x − 4. Find g(f(x)) in simplest form.
Answer: −15x − 22
- g(f(x)) = −3(5x + 6) − 4
- = −15x − 22
9.f(x) = 4x + 6 and g(x) = 5x + 5. Find f(g(x)) in simplest form.
Answer: 20x + 26
- f(g(x)) = 4(5x + 5) + 6
- = 20x + 26
10.f(x) = 4x + 2 and g(x) = −4x − 1. Find g(f(x)) in simplest form.
Answer: −16x − 9
- g(f(x)) = −4(4x + 2) − 1
- = −16x − 9
11.Find the inverse function of f(x) = 4x − 3.
Answer: f−1(x) =
- y = 4x − 3
- Swap x and y: x = 4y − 3
- Solve for y: y =
12.Find the inverse function of f(x) = −6x − 5.
Answer: f−1(x) =
- y = −6x − 5
- Swap x and y: x = −6y − 5
- Solve for y: y =
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