Let $f(x) = \sqrt{1-x}$ and $g(x)= \sqrt{25-x^{2}}.$ Find $f + g,$ $f - g,$ $f \cdot g,$ and $\displaystyle \frac{f}{g}$, and their respective domains.

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1. $f + g =$

2. What is the domain of $f + g$ ?
Answer (in interval notation):

3. $f - g =$

4. What is the domain of $f - g$ ?
Answer (in interval notation):

5. $f \cdot g =$

6. What is the domain of $f \cdot g$ ?
Answer (in interval notation):

7. $\displaystyle \frac{f}{g} =$

8. What is the domain of $\displaystyle \frac{f}{g}$ ?
Answer (in interval notation):

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