Year 10 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 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 and g(x) = −4x + 4. Find f(g(x)) in simplest form.
Answer: −16x + 16
- f(g(x)) = 4(−4x + 4)
- = −16x + 16
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.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 =
4.f(x) = 5x + 4 and g(x) = −4x + 1. Find g(f(x)) in simplest form.
Answer: −20x − 15
- g(f(x)) = −4(5x + 4) + 1
- = −20x − 15
5.f(x) = −x and g(x) = 3x + 6. Find g(f(x)) in simplest form.
Answer: −3x + 6
- g(f(x)) = 3(−x) + 6
- = −3x + 6
6.f(x) = 5x + 6 and g(x) = 2x − 1. Find g(f(x)) in simplest form.
Answer: 10x + 11
- g(f(x)) = 2(5x + 6) − 1
- = 10x + 11
7.Find the inverse function of f(x) = −x − 2.
Answer: f−1(x) = −x − 2
- y = −x − 2
- Swap x and y: x = −y − 2
- Solve for y: y = −x − 2
8.Find the inverse function of f(x) = −3x − 7.
Answer: f−1(x) =
- y = −3x − 7
- Swap x and y: x = −3y − 7
- Solve for y: y =
9.Find the inverse function of f(x) = 7x − 9.
Answer: f−1(x) =
- y = 7x − 9
- Swap x and y: x = 7y − 9
- Solve for y: y =
10.Find the inverse function of f(x) = x + 1.
Answer: f−1(x) = x − 1
- y = x + 1
- Swap x and y: x = y + 1
- Solve for y: y = x − 1
11.f(x) = 4x + 6 and g(x) = x − 5. Find f(g(x)) in simplest form.
Answer: 4x − 14
- f(g(x)) = 4(x − 5) + 6
- = 4x − 14
12.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 =
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