12th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 12th Grade functions worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Functions12th 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) = −4x − 3 and g(x) = 2x − 1. Find f(g(x)) in simplest form.
Answer: −8x + 1
- f(g(x)) = −4(2x − 1) − 3
- = −8x + 1
2.f(x) = x − 1 and g(x) = 5x + 3. Find f(g(x)) in simplest form.
Answer: 5x + 2
- f(g(x)) = 1(5x + 3) − 1
- = 5x + 2
3.f(x) = −3x − 4 and g(x) = −3x + 2. Find f(g(x)) in simplest form.
Answer: 9x − 10
- f(g(x)) = −3(−3x + 2) − 4
- = 9x − 10
4.f(x) = −3x − 1 and g(x) = 2x − 1. Find f(g(x)) in simplest form.
Answer: −6x + 2
- f(g(x)) = −3(2x − 1) − 1
- = −6x + 2
5.f(x) = 5x + 6 and g(x) = 5x − 3. Find f(g(x)) in simplest form.
Answer: 25x − 9
- f(g(x)) = 5(5x − 3) + 6
- = 25x − 9
6.f(x) = −4x + 3 and g(x) = 4x − 4. Find f(g(x)) in simplest form.
Answer: −16x + 19
- f(g(x)) = −4(4x − 4) + 3
- = −16x + 19
7.Find the inverse function of f(x) = 2x.
Answer: f−1(x) =
- y = 2x
- Swap x and y: x = 2y
- Solve for y: y =
8.f(x) = −3x − 2 and g(x) = 3x + 3. Find g(f(x)) in simplest form.
Answer: −9x − 3
- g(f(x)) = 3(−3x − 2) + 3
- = −9x − 3
9.f(x) = −4x + 1 and g(x) = 3x + 3. Find g(f(x)) in simplest form.
Answer: −12x + 6
- g(f(x)) = 3(−4x + 1) + 3
- = −12x + 6
10.f(x) = −2x − 6 and g(x) = −3x − 2. Find f(g(x)) in simplest form.
Answer: 6x − 2
- f(g(x)) = −2(−3x − 2) − 6
- = 6x − 2
11.Find the inverse function of f(x) = 5x + 9.
Answer: f−1(x) =
- y = 5x + 9
- Swap x and y: x = 5y + 9
- Solve for y: y =
12.f(x) = 3x − 6 and g(x) = −3x + 5. Find f(g(x)) in simplest form.
Answer: −9x + 9
- f(g(x)) = 3(−3x + 5) − 6
- = −9x + 9
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