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.f(x) = −4x + 6 and g(x) = 2x − 5. Find f(g(x)) in simplest form.
Answer: −8x + 26
- f(g(x)) = −4(2x − 5) + 6
- = −8x + 26
2.f(x) = 2x − 1 and g(x) = −4x + 3. Find f(g(x)) in simplest form.
Answer: −8x + 5
- f(g(x)) = 2(−4x + 3) − 1
- = −8x + 5
3.f(x) = x + 3 and g(x) = 5x. Find f(g(x)) in simplest form.
Answer: 5x + 3
- f(g(x)) = 1(5x) + 3
- = 5x + 3
4.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
5.Find the inverse function of f(x) = −x.
Answer: f−1(x) = −x
- y = −x
- Swap x and y: x = −y
- Solve for y: y = −x
6.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 =
7.f(x) = 3x − 6 and g(x) = 3x + 3. Find g(f(x)) in simplest form.
Answer: 9x − 15
- g(f(x)) = 3(3x − 6) + 3
- = 9x − 15
8.f(x) = 2x + 3 and g(x) = 4x + 5. Find f(g(x)) in simplest form.
Answer: 8x + 13
- f(g(x)) = 2(4x + 5) + 3
- = 8x + 13
9.f(x) = −3x − 1 and g(x) = 3x + 5. Find f(g(x)) in simplest form.
Answer: −9x − 16
- f(g(x)) = −3(3x + 5) − 1
- = −9x − 16
10.f(x) = 4x − 5 and g(x) = 4x + 3. Find g(f(x)) in simplest form.
Answer: 16x − 17
- g(f(x)) = 4(4x − 5) + 3
- = 16x − 17
11.f(x) = 5x − 6 and g(x) = 2x − 1. Find g(f(x)) in simplest form.
Answer: 10x − 13
- g(f(x)) = 2(5x − 6) − 1
- = 10x − 13
12.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 =
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