Year 10 Function Notation, Composites and Inverses Worksheet — Level 3 — 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 — 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) = 2x + 3 and g(x) = x + 1. Find f(g(x)) in simplest form.
Answer: 2x + 5
- f(g(x)) = 2(x + 1) + 3
- = 2x + 5
2.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 =
3.Find the inverse function of f(x) = −5x + 1.
Answer: f−1(x) =
- y = −5x + 1
- Swap x and y: x = −5y + 1
- Solve for y: y =
4.f(x) = 3x − 6 and g(x) = 2x + 5. Find f(g(x)) in simplest form.
Answer: 6x + 9
- f(g(x)) = 3(2x + 5) − 6
- = 6x + 9
5.Find the inverse function of f(x) = 7x + 5.
Answer: f−1(x) =
- y = 7x + 5
- Swap x and y: x = 7y + 5
- Solve for y: y =
6.f(x) = 2x + 2 and g(x) = −4x + 3. Find g(f(x)) in simplest form.
Answer: −8x − 5
- g(f(x)) = −4(2x + 2) + 3
- = −8x − 5
7.Find the inverse function of f(x) = −x − 9.
Answer: f−1(x) = −x − 9
- y = −x − 9
- Swap x and y: x = −y − 9
- Solve for y: y = −x − 9
8.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 =
9.f(x) = 2x + 1 and g(x) = −x. Find g(f(x)) in simplest form.
Answer: −2x − 1
- g(f(x)) = −1(2x + 1)
- = −2x − 1
10.f(x) = −3x − 2 and g(x) = x − 5. Find f(g(x)) in simplest form.
Answer: −3x + 13
- f(g(x)) = −3(x − 5) − 2
- = −3x + 13
11.f(x) = 5x − 3 and g(x) = x + 4. Find f(g(x)) in simplest form.
Answer: 5x + 17
- f(g(x)) = 5(x + 4) − 3
- = 5x + 17
12.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
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