Question

Domain of the function $\sqrt{2-x} - \frac{1}{\sqrt{9-x^2}}$ is

• A. (-3, 1)
• B. [-3, 1]
• C. (-3, 2]
• D. [-3, 1)

Answer 1

Answer: (C)

(-3, 2]

Answer 2

To find the domain of $f(x) = \sqrt{2-x} - \frac{1}{\sqrt{9-x^2}}$, we need to satisfy two conditions:

1. $2 - x \ge 0 \implies x \le 2$
2. $9 - x^2 > 0 \implies x^2 < 9 \implies -3 < x < 3$

The intersection of these two intervals is $(-3, 2]$.