Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · FunctionsYear 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 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 + 8.
Answer: f−1(x) =
- y = 3x + 8
- Swap x and y: x = 3y + 8
- Solve for y: y =
2.f(x) = 5x + 6 and g(x) = −x. Find g(f(x)) in simplest form.
Answer: −5x − 6
- g(f(x)) = −1(5x + 6)
- = −5x − 6
3.f(x) = −4x − 6 and g(x) = 4x − 5. Find f(g(x)) in simplest form.
Answer: −16x + 14
- f(g(x)) = −4(4x − 5) − 6
- = −16x + 14
4.f(x) = −4x − 3 and g(x) = 3x + 6. Find f(g(x)) in simplest form.
Answer: −12x − 27
- f(g(x)) = −4(3x + 6) − 3
- = −12x − 27
5.f(x) = x and g(x) = 5x − 2. Find g(f(x)) in simplest form.
Answer: 5x − 2
- g(f(x)) = 5(x) − 2
- = 5x − 2
6.f(x) = −x − 6 and g(x) = 3x + 6. Find g(f(x)) in simplest form.
Answer: −3x − 12
- g(f(x)) = 3(−x − 6) + 6
- = −3x − 12
7.Find the inverse function of f(x) = −5x − 1.
Answer: f−1(x) =
- y = −5x − 1
- Swap x and y: x = −5y − 1
- Solve for y: y =
8.f(x) = 2x + 5 and g(x) = 3x − 6. Find f(g(x)) in simplest form.
Answer: 6x − 7
- f(g(x)) = 2(3x − 6) + 5
- = 6x − 7
9.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 =
10.Find the inverse function of f(x) = −2x − 2.
Answer: f−1(x) =
- y = −2x − 2
- Swap x and y: x = −2y − 2
- Solve for y: y =
11.Find the inverse function of f(x) = x − 7.
Answer: f−1(x) = x + 7
- y = x − 7
- Swap x and y: x = y − 7
- Solve for y: y = x + 7
12.f(x) = −4x + 3 and g(x) = 3x − 4. Find g(f(x)) in simplest form.
Answer: −12x + 5
- g(f(x)) = 3(−4x + 3) − 4
- = −12x + 5
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