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Q.
The set of all $x$ for which $f(x)=\log _{\frac{x-2}{x+3}} 2$ and $g(x)=\frac{1}{\sqrt{x^2-9}}$ are both not defined is
Relations and Functions
Solution:
The function $f$ is not defined for $-3 \leq x \leq$ 2 and $g$ is not defined for those $x$ for which $x^2-9 \leq 0$ i.e., $x \in[-3,3]$.
Thus $f$ and $g$ are not defined on $[-3,2]$.