10th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 10th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Functions10th Grade 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) = −3x − 4 and g(x) = −x + 3. Find g(f(x)) in simplest form.
Answer: 3x + 7
- g(f(x)) = −1(−3x − 4) + 3
- = 3x + 7
2.Find the inverse function of f(x) = −3x + 5.
Answer: f−1(x) =
- y = −3x + 5
- Swap x and y: x = −3y + 5
- Solve for y: y =
3.f(x) = −3x − 3 and g(x) = 3x + 5. Find f(g(x)) in simplest form.
Answer: −9x − 18
- f(g(x)) = −3(3x + 5) − 3
- = −9x − 18
4.f(x) = x − 3 and g(x) = 2x. Find f(g(x)) in simplest form.
Answer: 2x − 3
- f(g(x)) = 1(2x) − 3
- = 2x − 3
5.Find the inverse function of f(x) = 7x − 8.
Answer: f−1(x) =
- y = 7x − 8
- Swap x and y: x = 7y − 8
- Solve for y: y =
6.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 =
7.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 =
8.Find the inverse function of f(x) = −4x + 1.
Answer: f−1(x) =
- y = −4x + 1
- Swap x and y: x = −4y + 1
- Solve for y: y =
9.Find the inverse function of f(x) = −5x.
Answer: f−1(x) = −
- y = −5x
- Swap x and y: x = −5y
- Solve for y: y = −
10.f(x) = 4x + 3 and g(x) = 3x. Find f(g(x)) in simplest form.
Answer: 12x + 3
- f(g(x)) = 4(3x) + 3
- = 12x + 3
11.Find the inverse function of f(x) = −6x − 2.
Answer: f−1(x) =
- y = −6x − 2
- Swap x and y: x = −6y − 2
- Solve for y: y =
12.Find the inverse function of f(x) = 3x − 9.
Answer: f−1(x) =
- y = 3x − 9
- Swap x and y: x = 3y − 9
- Solve for y: y =
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