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