Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 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 3 — Practice Set 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.f(x) = 4x − 1 and g(x) = 5x − 5. Find f(g(x)) in simplest form.
Answer: 20x − 21
- f(g(x)) = 4(5x − 5) − 1
- = 20x − 21
2.Find the inverse function of f(x) = 5x − 7.
Answer: f−1(x) =
- y = 5x − 7
- Swap x and y: x = 5y − 7
- Solve for y: y =
3.f(x) = 5x − 2 and g(x) = −x + 6. Find g(f(x)) in simplest form.
Answer: −5x + 8
- g(f(x)) = −1(5x − 2) + 6
- = −5x + 8
4.f(x) = −2x + 5 and g(x) = 3x − 4. Find g(f(x)) in simplest form.
Answer: −6x + 11
- g(f(x)) = 3(−2x + 5) − 4
- = −6x + 11
5.f(x) = 3x + 1 and g(x) = −2x − 4. Find g(f(x)) in simplest form.
Answer: −6x − 6
- g(f(x)) = −2(3x + 1) − 4
- = −6x − 6
6.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
7.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 =
8.f(x) = −2x + 5 and g(x) = −4x + 1. Find g(f(x)) in simplest form.
Answer: 8x − 19
- g(f(x)) = −4(−2x + 5) + 1
- = 8x − 19
9.Find the inverse function of f(x) = −4x − 1.
Answer: f−1(x) =
- y = −4x − 1
- Swap x and y: x = −4y − 1
- Solve for y: y =
10.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 =
11.Find the inverse function of f(x) = −x + 8.
Answer: f−1(x) = −x + 8
- y = −x + 8
- Swap x and y: x = −y + 8
- Solve for y: y = −x + 8
12.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 =
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