Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 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 — 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.f(x) = −2x + 4 and g(x) = 4x − 3. Find f(g(x)) in simplest form.
Answer: −8x + 10
- f(g(x)) = −2(4x − 3) + 4
- = −8x + 10
2.Find the inverse function of f(x) = 7x − 4.
Answer: f−1(x) =
- y = 7x − 4
- Swap x and y: x = 7y − 4
- Solve for y: y =
3.f(x) = x − 6 and g(x) = −4x. Find g(f(x)) in simplest form.
Answer: −4x + 24
- g(f(x)) = −4(x − 6)
- = −4x + 24
4.f(x) = 3x − 2 and g(x) = 5x − 2. Find g(f(x)) in simplest form.
Answer: 15x − 12
- g(f(x)) = 5(3x − 2) − 2
- = 15x − 12
5.Find the inverse function of f(x) = −6x + 1.
Answer: f−1(x) =
- y = −6x + 1
- Swap x and y: x = −6y + 1
- Solve for y: y =
6.Find the inverse function of f(x) = −4x − 7.
Answer: f−1(x) =
- y = −4x − 7
- Swap x and y: x = −4y − 7
- Solve for y: y =
7.f(x) = 5x − 2 and g(x) = −x + 1. Find f(g(x)) in simplest form.
Answer: −5x + 3
- f(g(x)) = 5(−x + 1) − 2
- = −5x + 3
8.f(x) = x + 5 and g(x) = −2x + 6. Find g(f(x)) in simplest form.
Answer: −2x − 4
- g(f(x)) = −2(x + 5) + 6
- = −2x − 4
9.f(x) = 4x + 4 and g(x) = −4x − 3. Find g(f(x)) in simplest form.
Answer: −16x − 19
- g(f(x)) = −4(4x + 4) − 3
- = −16x − 19
10.Find the inverse function of f(x) = 7x + 9.
Answer: f−1(x) =
- y = 7x + 9
- Swap x and y: x = 7y + 9
- Solve for y: y =
11.f(x) = −3x − 6 and g(x) = 5x − 3. Find g(f(x)) in simplest form.
Answer: −15x − 33
- g(f(x)) = 5(−3x − 6) − 3
- = −15x − 33
12.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
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