JEE MAIN - Mathematics (2023 - 29th January Morning Shift - No. 13)
The domain of $$f(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R}$$ is
$$( - 1,\infty ) - \{ 3\} $$
$$\mathbb{R} - \{ - 1,3)$$
$$(2,\infty ) - \{ 3\} $$
$$\mathbb{R} - \{ 3\} $$
Explanation
$x-2>0 \Rightarrow x>2$
$\mathrm{x}+1>0 \Rightarrow \mathrm{x}>-1$
$x+1 \neq 1 \Rightarrow x \neq 0$ and $x>0$
Denominator
$\mathrm{x}^{2}-2 \mathrm{x}-3 \neq 0$
$(x-3)(x+1) \neq 0$
$\mathrm{x} \neq-1,3$
So Ans $(2, \infty)-\{3\}$
$\mathrm{x}+1>0 \Rightarrow \mathrm{x}>-1$
$x+1 \neq 1 \Rightarrow x \neq 0$ and $x>0$
Denominator
$\mathrm{x}^{2}-2 \mathrm{x}-3 \neq 0$
$(x-3)(x+1) \neq 0$
$\mathrm{x} \neq-1,3$
So Ans $(2, \infty)-\{3\}$
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