Question

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

• A. $(2,\infty )-\{3\}$
• B. $R-\{3\}$
• C. $R-\{-1,3\}$
• D. $(-1,\infty )-\{3\}$

Answer 1

Answer: (A)

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