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  4. The domain of f(x)=( log (x+1)(x-2)/e2 log e x-(2 x+3)), x ∈ R is

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Q. The domain of $f(x)=\frac{\log _{(x+1)}(x-2)}{e^{2 \log _e x}-(2 x+3)}, x \in R$ is

JEE MainJEE Main 2023Relations and Functions

Solution:

$x-2>0 \Rightarrow x>2$
$x+1>0 \Rightarrow x>-1 $
$ x+1 \neq 1 \Rightarrow x \neq 0 \text { and } x>0$
Denominator
$ x^2-2 x-3 \neq 0 $
$ (x-3)(x+1) \neq 0$
$x \neq-1,3$
So Ans $(2, \infty)-\{3\}$