10th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — 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 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.f(x) = 5x − 2 and g(x) = 3x − 3. Find g(f(x)) in simplest form.
Answer: 15x − 9
- g(f(x)) = 3(5x − 2) − 3
- = 15x − 9
2.f(x) = −4x − 6 and g(x) = 5x + 6. Find f(g(x)) in simplest form.
Answer: −20x − 30
- f(g(x)) = −4(5x + 6) − 6
- = −20x − 30
3.f(x) = 5x − 6 and g(x) = 4x + 1. Find g(f(x)) in simplest form.
Answer: 20x − 23
- g(f(x)) = 4(5x − 6) + 1
- = 20x − 23
4.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 =
5.f(x) = −2x − 2 and g(x) = x + 5. Find f(g(x)) in simplest form.
Answer: −2x − 12
- f(g(x)) = −2(x + 5) − 2
- = −2x − 12
6.f(x) = −x + 1 and g(x) = 5x + 5. Find g(f(x)) in simplest form.
Answer: −5x + 10
- g(f(x)) = 5(−x + 1) + 5
- = −5x + 10
7.f(x) = x + 5 and g(x) = 3x + 4. Find g(f(x)) in simplest form.
Answer: 3x + 19
- g(f(x)) = 3(x + 5) + 4
- = 3x + 19
8.Find the inverse function of f(x) = x − 9.
Answer: f−1(x) = x + 9
- y = x − 9
- Swap x and y: x = y − 9
- Solve for y: y = x + 9
9.f(x) = −x + 2 and g(x) = 5x − 2. Find g(f(x)) in simplest form.
Answer: −5x + 8
- g(f(x)) = 5(−x + 2) − 2
- = −5x + 8
10.f(x) = x + 5 and g(x) = 5x + 2. Find g(f(x)) in simplest form.
Answer: 5x + 27
- g(f(x)) = 5(x + 5) + 2
- = 5x + 27
11.Find the inverse function of f(x) = −3x + 2.
Answer: f−1(x) =
- y = −3x + 2
- Swap x and y: x = −3y + 2
- Solve for y: y =
12.f(x) = −4x + 4 and g(x) = 2x − 2. Find g(f(x)) in simplest form.
Answer: −8x + 6
- g(f(x)) = 2(−4x + 4) − 2
- = −8x + 6
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