Question
Suppose \( f(5)=-9 \) and \( g(5)=-3 \). Find the following. \( (f+g)(5)=\square \) \( (f-g)(5)=\square \) \( (f g)(5)=\square \) \( \left(\frac{f}{g}\right)(5)=\square \)
Ask by Rojas Gross. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(f+g)(5) = -12
(f-g)(5) = -6
(fg)(5) = 27
(f/g)(5) = 3
Solution
We are given that f(5) = -9 and g(5) = -3.
1. (f+g)(5) = f(5) + g(5) = -9 + (-3) = -12
2. (f-g)(5) = f(5) - g(5) = -9 - (-3) = -9 + 3 = -6
3. (fg)(5) = f(5) · g(5) = (-9) · (-3) = 27
4. (f/g)(5) = f(5) / g(5) = (-9) / (-3) = 3
Thus, the answers are:
(f+g)(5) = -12
(f-g)(5) = -6
(fg)(5) = 27
(f/g)(5) = 3
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find the values, we will apply the definitions of the functions \( f \) and \( g \) and the operations indicated. 1. **For \( (f+g)(5) \)**: \[ (f + g)(5) = f(5) + g(5) = -9 + (-3) = -9 - 3 = -12 \] 2. **For \( (f-g)(5) \)**: \[ (f - g)(5) = f(5) - g(5) = -9 - (-3) = -9 + 3 = -6 \] 3. **For \( (fg)(5) \)**: \[ (fg)(5) = f(5) \cdot g(5) = -9 \cdot (-3) = 27 \] 4. **For \( \left(\frac{f}{g}\right)(5) \)**: \[ \left(\frac{f}{g}\right)(5) = \frac{f(5)}{g(5)} = \frac{-9}{-3} = 3 \] Now, summary of values: \[ (f+g)(5) = -12, \quad (f-g)(5) = -6, \quad (fg)(5) = 27, \quad \left(\frac{f}{g}\right)(5) = 3 \]
