Question:
The domain of the real function $f(x)=\frac{x}{\sqrt{9-x^{2}}}$ is ___________.
Solution:
Given: $f(x)=\frac{x}{\sqrt{9-x^{2}}}$
To find the domain, we find the real values of x for which the function is defined.
$x \in R$ and $9-x^{2}>0$
$\Rightarrow x \in R$ and $9>x^{2}$
$\Rightarrow x \in R$ and $x^{2}<9$
$\Rightarrow x \in R$ and $-3
$\Rightarrow-3
$\Rightarrow x \in(-3,3)$
Hence, the domain of the real function $f(x)=\frac{x}{\sqrt{9-x^{2}}}$ is $(-3,3)$.
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