Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
Below is the transcription of the image content, designed for an educational website: --- ## Function Operations and Domains **Find \( f + g \), \( f - g \), \( fg \), and \( \frac{f}{g} \) and their domains.** Given functions: \[ f(x) = x, \quad g(x) = 3x \] ### Tasks 1. **Find \((f + g)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 2. **Find the domain of \((f + g)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 3. **Find \((f - g)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 4. **Find the domain of \((f - g)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 5. **Find \((fg)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 6. **Find the domain of \((fg)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 7. **Find \(\left(\frac{f}{g}\right)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 8. **Find the domain of \(\left(\frac{f}{g}\right)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] --- This content adequately presents the math problems and leaves space for students to input their answers. The problem description provides both the given functions and clear instructions on what students need to find, emphasizing the use of interval notation for domain answers.
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Transcribed Image Text:Below is the transcription of the image content, designed for an educational website: --- ## Function Operations and Domains **Find \( f + g \), \( f - g \), \( fg \), and \( \frac{f}{g} \) and their domains.** Given functions: \[ f(x) = x, \quad g(x) = 3x \] ### Tasks 1. **Find \((f + g)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 2. **Find the domain of \((f + g)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 3. **Find \((f - g)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 4. **Find the domain of \((f - g)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 5. **Find \((fg)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 6. **Find the domain of \((fg)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] 7. **Find \(\left(\frac{f}{g}\right)(x)\).** \[\_\_\_\_\_\_\_\_\_\_\_\_\] 8. **Find the domain of \(\left(\frac{f}{g}\right)(x)\)**. (Enter your answer using interval notation.) \[\_\_\_\_\_\_\_\_\_\_\_\_\] --- This content adequately presents the math problems and leaves space for students to input their answers. The problem description provides both the given functions and clear instructions on what students need to find, emphasizing the use of interval notation for domain answers.
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