Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — 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 4 — 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.f(x) = 2x − 3 and g(x) = 5x. Find f(g(x)) in simplest form.
Answer: 10x − 3
- f(g(x)) = 2(5x) − 3
- = 10x − 3
3.f(x) = 5x − 3 and g(x) = −4x − 6. Find f(g(x)) in simplest form.
Answer: −20x − 33
- f(g(x)) = 5(−4x − 6) − 3
- = −20x − 33
4.f(x) = −3x and g(x) = 4x. Find f(g(x)) in simplest form.
Answer: −12x
- f(g(x)) = −3(4x)
- = −12x
5.Find the inverse function of f(x) = 5x.
Answer: f−1(x) =
- y = 5x
- Swap x and y: x = 5y
- Solve for y: y =
6.f(x) = 2x and g(x) = −3x − 4. Find f(g(x)) in simplest form.
Answer: −6x − 8
- f(g(x)) = 2(−3x − 4)
- = −6x − 8
7.f(x) = −2x − 2 and g(x) = −x + 2. Find f(g(x)) in simplest form.
Answer: 2x − 6
- f(g(x)) = −2(−x + 2) − 2
- = 2x − 6
8.Find the inverse function of f(x) = 5x + 7.
Answer: f−1(x) =
- y = 5x + 7
- Swap x and y: x = 5y + 7
- Solve for y: y =
9.Find the inverse function of f(x) = −6x − 9.
Answer: f−1(x) =
- y = −6x − 9
- Swap x and y: x = −6y − 9
- Solve for y: y =
10.Find the inverse function of f(x) = 5x + 9.
Answer: f−1(x) =
- y = 5x + 9
- Swap x and y: x = 5y + 9
- Solve for y: y =
11.f(x) = −2x − 4 and g(x) = 3x + 3. Find f(g(x)) in simplest form.
Answer: −6x − 10
- f(g(x)) = −2(3x + 3) − 4
- = −6x − 10
12.f(x) = 5x − 6 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: 5x + 19
- f(g(x)) = 5(x + 5) − 6
- = 5x + 19
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