Verified Solution • 2025–26 Session moderate

QJEEM23Ma1d32: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1d32 Solution: The domain of is

The domain of f(x)=log⁡(x+1)(x−2)e2log⁡ex−(2x+3),x∈Rf(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R} is

Multiple Choice Options

  • A (−1,∞)−{3}( - 1,\infty ) - \{ 3\}
  • B R−{−1,3)\mathbb{R} - \{ - 1,3)
  • C (2,∞)−{3}(2,\infty ) - \{ 3\}
  • D R−{3}\mathbb{R} - \{ 3\}

Step-by-Step Verified Solution

x-2>0 \Rightarrow x>2

\mathrm{x}+1>0 \Rightarrow \mathrm{x}>-1

x+1≠1⇒x≠0x+1 \neq 1 \Rightarrow x \neq 0 and x>0

Denominator

x2−2x−3≠0\mathrm{x}^{2}-2 \mathrm{x}-3 \neq 0

(x−3)(x+1)≠0(x-3)(x+1) \neq 0

x≠−1,3\mathrm{x} \neq-1,3

So Ans (2,∞)−{3}(2, \infty)-\{3\}

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