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.Find the inverse function of f(x) = 7x − 4.
Answer: f−1(x) =
- y = 7x − 4
- Swap x and y: x = 7y − 4
- Solve for y: y =
2.Find the inverse function of f(x) = −4x − 5.
Answer: f−1(x) =
- y = −4x − 5
- Swap x and y: x = −4y − 5
- Solve for y: y =
3.f(x) = 3x + 3 and g(x) = −x − 6. Find g(f(x)) in simplest form.
Answer: −3x − 9
- g(f(x)) = −1(3x + 3) − 6
- = −3x − 9
4.f(x) = 2x − 6 and g(x) = 2x − 6. Find g(f(x)) in simplest form.
Answer: 4x − 18
- g(f(x)) = 2(2x − 6) − 6
- = 4x − 18
5.f(x) = x − 6 and g(x) = −3x − 5. Find g(f(x)) in simplest form.
Answer: −3x + 13
- g(f(x)) = −3(x − 6) − 5
- = −3x + 13
6.Find the inverse function of f(x) = 6x + 7.
Answer: f−1(x) =
- y = 6x + 7
- Swap x and y: x = 6y + 7
- Solve for y: y =
7.Find the inverse function of f(x) = 4x − 2.
Answer: f−1(x) =
- y = 4x − 2
- Swap x and y: x = 4y − 2
- Solve for y: y =
8.f(x) = 4x − 1 and g(x) = −4x − 5. Find g(f(x)) in simplest form.
Answer: −16x − 1
- g(f(x)) = −4(4x − 1) − 5
- = −16x − 1
9.Find the inverse function of f(x) = 5x − 8.
Answer: f−1(x) =
- y = 5x − 8
- Swap x and y: x = 5y − 8
- Solve for y: y =
10.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 =
11.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 =
12.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 =
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