Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — 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 — 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) = −4x + 2. Find f(g(x)) in simplest form.
Answer: 16x − 2
- f(g(x)) = −4(−4x + 2) + 6
- = 16x − 2
2.f(x) = 3x and g(x) = x + 4. Find g(f(x)) in simplest form.
Answer: 3x + 4
- g(f(x)) = 1(3x) + 4
- = 3x + 4
3.Find the inverse function of f(x) = −x − 6.
Answer: f−1(x) = −x − 6
- y = −x − 6
- Swap x and y: x = −y − 6
- Solve for y: y = −x − 6
4.Find the inverse function of f(x) = 5x.
Answer: f−1(x) =
- y = 5x
- Swap x and y: x = 5y
- Solve for y: y =
5.Find the inverse function of f(x) = 3x + 4.
Answer: f−1(x) =
- y = 3x + 4
- Swap x and y: x = 3y + 4
- Solve for y: y =
6.f(x) = 5x − 4 and g(x) = −3x − 1. Find g(f(x)) in simplest form.
Answer: −15x + 11
- g(f(x)) = −3(5x − 4) − 1
- = −15x + 11
7.f(x) = 3x − 6 and g(x) = 2x − 2. Find g(f(x)) in simplest form.
Answer: 6x − 14
- g(f(x)) = 2(3x − 6) − 2
- = 6x − 14
8.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 =
9.f(x) = −4x + 2 and g(x) = −x + 6. Find g(f(x)) in simplest form.
Answer: 4x + 4
- g(f(x)) = −1(−4x + 2) + 6
- = 4x + 4
10.f(x) = −x and g(x) = 3x + 6. Find f(g(x)) in simplest form.
Answer: −3x − 6
- f(g(x)) = −1(3x + 6)
- = −3x − 6
11.f(x) = −4x − 5 and g(x) = 3x. Find g(f(x)) in simplest form.
Answer: −12x − 15
- g(f(x)) = 3(−4x − 5)
- = −12x − 15
12.f(x) = −x − 4 and g(x) = −4x − 5. Find f(g(x)) in simplest form.
Answer: 4x + 1
- f(g(x)) = −1(−4x − 5) − 4
- = 4x + 1
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