10th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — 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 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) = 7x.
Answer: f−1(x) =
- y = 7x
- Swap x and y: x = 7y
- Solve for y: y =
2.f(x) = x + 4 and g(x) = 2x − 4. Find f(g(x)) in simplest form.
Answer: 2x
- f(g(x)) = 1(2x − 4) + 4
- = 2x
3.Find the inverse function of f(x) = x + 5.
Answer: f−1(x) = x − 5
- y = x + 5
- Swap x and y: x = y + 5
- Solve for y: y = x − 5
4.Find the inverse function of f(x) = −6x + 8.
Answer: f−1(x) =
- y = −6x + 8
- Swap x and y: x = −6y + 8
- Solve for y: y =
5.f(x) = 4x − 3 and g(x) = x + 1. Find f(g(x)) in simplest form.
Answer: 4x + 1
- f(g(x)) = 4(x + 1) − 3
- = 4x + 1
6.f(x) = −x − 1 and g(x) = x + 4. Find f(g(x)) in simplest form.
Answer: −x − 5
- f(g(x)) = −1(x + 4) − 1
- = −x − 5
7.f(x) = −3x − 4 and g(x) = 5x + 6. Find f(g(x)) in simplest form.
Answer: −15x − 22
- f(g(x)) = −3(5x + 6) − 4
- = −15x − 22
8.f(x) = −4x + 4 and g(x) = −4x + 2. Find f(g(x)) in simplest form.
Answer: 16x − 4
- f(g(x)) = −4(−4x + 2) + 4
- = 16x − 4
9.Find the inverse function of f(x) = −3x − 7.
Answer: f−1(x) =
- y = −3x − 7
- Swap x and y: x = −3y − 7
- Solve for y: y =
10.f(x) = x + 1 and g(x) = 5x − 6. Find g(f(x)) in simplest form.
Answer: 5x − 1
- g(f(x)) = 5(x + 1) − 6
- = 5x − 1
11.Find the inverse function of f(x) = 6x − 5.
Answer: f−1(x) =
- y = 6x − 5
- Swap x and y: x = 6y − 5
- Solve for y: y =
12.Find the inverse function of f(x) = −x − 2.
Answer: f−1(x) = −x − 2
- y = −x − 2
- Swap x and y: x = −y − 2
- Solve for y: y = −x − 2
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