The domain of the function f ( x ) = 1 9 - x 2 is

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Solution

Q.
The domain of the function $f (x) = \frac{1}{\sqrt{9 - x^{2}}}$ is

1 $- 3 \leq x \leq 3$

2 $- 3 < x < 3$

3 $- 9 \leq x \leq 9$

4 $- 9 < x < 9$

Ans.
(2)

$f (x) = \frac{1}{\sqrt{9 - x^{2}}}$

$Clearly, 9 - x^{2} > 0 \Rightarrow x^{2} - 9 < 0$

$\Rightarrow$ $(x + 3) (x - 3) < 0 .$ Thus domain of $f (x)$ is $(- 3, 3)$ .

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