11th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 11th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Functions11th 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) = −4x − 2 and g(x) = 2x − 2. Find g(f(x)) in simplest form.
Answer: −8x − 6
- g(f(x)) = 2(−4x − 2) − 2
- = −8x − 6
2.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 =
3.f(x) = 2x + 6 and g(x) = x − 2. Find f(g(x)) in simplest form.
Answer: 2x + 2
- f(g(x)) = 2(x − 2) + 6
- = 2x + 2
4.f(x) = −3x + 2 and g(x) = −x + 1. Find g(f(x)) in simplest form.
Answer: 3x − 1
- g(f(x)) = −1(−3x + 2) + 1
- = 3x − 1
5.f(x) = −2x + 5 and g(x) = −3x − 1. Find g(f(x)) in simplest form.
Answer: 6x − 16
- g(f(x)) = −3(−2x + 5) − 1
- = 6x − 16
6.f(x) = −4x + 4 and g(x) = −2x + 2. Find f(g(x)) in simplest form.
Answer: 8x − 4
- f(g(x)) = −4(−2x + 2) + 4
- = 8x − 4
7.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 =
8.f(x) = −3x + 6 and g(x) = 5x + 2. Find f(g(x)) in simplest form.
Answer: −15x
- f(g(x)) = −3(5x + 2) + 6
- = −15x
9.f(x) = −3x + 1 and g(x) = 3x − 3. Find f(g(x)) in simplest form.
Answer: −9x + 10
- f(g(x)) = −3(3x − 3) + 1
- = −9x + 10
10.f(x) = −3x and g(x) = x − 1. Find f(g(x)) in simplest form.
Answer: −3x + 3
- f(g(x)) = −3(x − 1)
- = −3x + 3
11.f(x) = −x + 5 and g(x) = −3x − 3. Find f(g(x)) in simplest form.
Answer: 3x + 8
- f(g(x)) = −1(−3x − 3) + 5
- = 3x + 8
12.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 =
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