Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 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) = −3x − 3.
Answer: f−1(x) =
- y = −3x − 3
- Swap x and y: x = −3y − 3
- Solve for y: y =
2.Find the inverse function of f(x) = −2x + 8.
Answer: f−1(x) =
- y = −2x + 8
- Swap x and y: x = −2y + 8
- Solve for y: y =
3.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 =
4.f(x) = −3x + 1 and g(x) = −3x. Find g(f(x)) in simplest form.
Answer: 9x − 3
- g(f(x)) = −3(−3x + 1)
- = 9x − 3
5.f(x) = 4x + 4 and g(x) = −2x − 4. Find g(f(x)) in simplest form.
Answer: −8x − 12
- g(f(x)) = −2(4x + 4) − 4
- = −8x − 12
6.f(x) = −2x + 4 and g(x) = 5x + 6. Find g(f(x)) in simplest form.
Answer: −10x + 26
- g(f(x)) = 5(−2x + 4) + 6
- = −10x + 26
7.f(x) = 2x and g(x) = x + 3. Find g(f(x)) in simplest form.
Answer: 2x + 3
- g(f(x)) = 1(2x) + 3
- = 2x + 3
8.Find the inverse function of f(x) = −4x − 6.
Answer: f−1(x) =
- y = −4x − 6
- Swap x and y: x = −4y − 6
- Solve for y: y =
9.Find the inverse function of f(x) = x − 3.
Answer: f−1(x) = x + 3
- y = x − 3
- Swap x and y: x = y − 3
- Solve for y: y = x + 3
10.Find the inverse function of f(x) = 3x − 5.
Answer: f−1(x) =
- y = 3x − 5
- Swap x and y: x = 3y − 5
- Solve for y: y =
11.f(x) = 4x and g(x) = −x + 4. Find g(f(x)) in simplest form.
Answer: −4x + 4
- g(f(x)) = −1(4x) + 4
- = −4x + 4
12.Find the inverse function of f(x) = 6x + 5.
Answer: f−1(x) =
- y = 6x + 5
- Swap x and y: x = 6y + 5
- Solve for y: y =
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