Given f(x)= a) (f + g)(x) c) (f - g)(x) 5x x-4 e) (f. g)(x) and g(x)= b) the domain of (f + g)(x) in interval notation g) 2) (1) (²) 6 x + 2 h) the domain of find the following. 5x2 + 16x-24 x²2x 8 d) the domain of (f - g)(x) in interval notation (1)(₂ 5x2 + 4x + 24 x² 2x 8 (-∞,-2) U (-2,4) U (4,00)✓ f) the domain of (f g)(x) in interval notation 30x (x-4)(x+2) می ۔ (-∞,-2) U (-2,4) U (4,00)✓ o ✓ (x) in interval notation (-00,-2) U (-2,4) U (4,00)✓
Given f(x)= a) (f + g)(x) c) (f - g)(x) 5x x-4 e) (f. g)(x) and g(x)= b) the domain of (f + g)(x) in interval notation g) 2) (1) (²) 6 x + 2 h) the domain of find the following. 5x2 + 16x-24 x²2x 8 d) the domain of (f - g)(x) in interval notation (1)(₂ 5x2 + 4x + 24 x² 2x 8 (-∞,-2) U (-2,4) U (4,00)✓ f) the domain of (f g)(x) in interval notation 30x (x-4)(x+2) می ۔ (-∞,-2) U (-2,4) U (4,00)✓ o ✓ (x) in interval notation (-00,-2) U (-2,4) U (4,00)✓
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Exploring Function Operations and Their Domains
Given the functions:
\[ f(x) = \frac{5x}{x-4} \quad \text{and} \quad g(x) = \frac{6}{x+2} \]
we need to find various operations of these functions and their corresponding domains.
---
#### a) \((f + g)(x)\)
\[ (f + g)(x) = \frac{5x^2 + 16x - 24}{x^2 - 2x - 8} \]
---
#### b) The domain of \((f + g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### c) \((f - g)(x)\)
\[ (f - g)(x) = \frac{5x^2 + 4x + 24}{x^2 - 2x - 8} \]
---
#### d) The domain of \((f - g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### e) \((f \cdot g)(x)\)
\[ (f \cdot g)(x) = \frac{30x}{(x-4)(x+2)} \]
---
#### f) The domain of \((f \cdot g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### g) \(\left( \frac{f}{g} \right)(x)\)
Work for this needs to be done to determine the result.
---
#### h) The domain of \(\left( \frac{f}{g} \right)(x)\) in interval notation
Work for this needs to be done to determine the result.
---
### Explanation of Notations and Operations
- **Function Addition (\(f + g\))**: This involves adding the expressions of \(f(x)\) and \(g(x)\) and simplifying if possible.
- **Function Subtraction (\(f - g\))**: This involves subtracting the expressions of \(g(x)\) from \(f](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11649eeb-c1d7-47bf-9022-208e8666dc61%2Fb5234e30-fa05-4b10-b2f2-38269e6c66d0%2Fx3hcfeyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exploring Function Operations and Their Domains
Given the functions:
\[ f(x) = \frac{5x}{x-4} \quad \text{and} \quad g(x) = \frac{6}{x+2} \]
we need to find various operations of these functions and their corresponding domains.
---
#### a) \((f + g)(x)\)
\[ (f + g)(x) = \frac{5x^2 + 16x - 24}{x^2 - 2x - 8} \]
---
#### b) The domain of \((f + g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### c) \((f - g)(x)\)
\[ (f - g)(x) = \frac{5x^2 + 4x + 24}{x^2 - 2x - 8} \]
---
#### d) The domain of \((f - g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### e) \((f \cdot g)(x)\)
\[ (f \cdot g)(x) = \frac{30x}{(x-4)(x+2)} \]
---
#### f) The domain of \((f \cdot g)(x)\) in interval notation
\[ (-\infty, -2) \cup (-2, 4) \cup (4, \infty) \]
---
#### g) \(\left( \frac{f}{g} \right)(x)\)
Work for this needs to be done to determine the result.
---
#### h) The domain of \(\left( \frac{f}{g} \right)(x)\) in interval notation
Work for this needs to be done to determine the result.
---
### Explanation of Notations and Operations
- **Function Addition (\(f + g\))**: This involves adding the expressions of \(f(x)\) and \(g(x)\) and simplifying if possible.
- **Function Subtraction (\(f - g\))**: This involves subtracting the expressions of \(g(x)\) from \(f
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