Sets, Relations & Functions
Domain of Functions
nta_pyq_2023_jan
Grade 11
Question:
The domain of $f(x) = \dfrac{\log_{(x+1)}(x-2)}{e^{2\log_e x} - (2x+3)}$, $x \in \mathbb{R}$ is
R - {1-3}
(2, ∞) - {3}
(-1, ∞) - {3}
R - {3}
Step-by-Step Solution
Key Concept: Require $x-2>0$, $x+1>0$, $x+1\ne1$, denominator $x^2-(2x+3)\ne0$.
$x>2$ (from $x-2>0$) and $x\ne3$ (from denominator $x^2-2x-3=(x-3)(x+1)\ne0$). Domain: $(2,\infty)-\{3\}$.
Correct Answer: 2