Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · FunctionsYear 11 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.f(x) = x + 2 and g(x) = −4x − 1. Find f(g(x)) in simplest form.
Answer: −4x + 1
- f(g(x)) = 1(−4x − 1) + 2
- = −4x + 1
2.f(x) = 5x − 3 and g(x) = −4x − 1. Find f(g(x)) in simplest form.
Answer: −20x − 8
- f(g(x)) = 5(−4x − 1) − 3
- = −20x − 8
3.f(x) = 2x − 2 and g(x) = 3x − 4. Find g(f(x)) in simplest form.
Answer: 6x − 10
- g(f(x)) = 3(2x − 2) − 4
- = 6x − 10
4.f(x) = 5x − 5 and g(x) = −3x + 2. Find g(f(x)) in simplest form.
Answer: −15x + 17
- g(f(x)) = −3(5x − 5) + 2
- = −15x + 17
5.f(x) = 4x + 1 and g(x) = −2x − 1. Find f(g(x)) in simplest form.
Answer: −8x − 3
- f(g(x)) = 4(−2x − 1) + 1
- = −8x − 3
6.f(x) = −3x − 1 and g(x) = −3x + 3. Find g(f(x)) in simplest form.
Answer: 9x + 6
- g(f(x)) = −3(−3x − 1) + 3
- = 9x + 6
7.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 =
8.Find the inverse function of f(x) = −4x + 3.
Answer: f−1(x) =
- y = −4x + 3
- Swap x and y: x = −4y + 3
- Solve for y: y =
9.f(x) = −3x − 4 and g(x) = −2x + 2. Find f(g(x)) in simplest form.
Answer: 6x − 10
- f(g(x)) = −3(−2x + 2) − 4
- = 6x − 10
10.f(x) = 2x − 6 and g(x) = −2x − 3. Find g(f(x)) in simplest form.
Answer: −4x + 9
- g(f(x)) = −2(2x − 6) − 3
- = −4x + 9
11.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 =
12.f(x) = 3x − 1 and g(x) = x + 3. Find g(f(x)) in simplest form.
Answer: 3x + 2
- g(f(x)) = 1(3x − 1) + 3
- = 3x + 2
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