Question

The domain of definition of the function $y=3e^{\sqrt{x^{2} - 1}}log \left(x - 1\right)$ is

• A. $\left(1 , \, \infty\right)$
• B. $1 , \infty$
• C. $R-\left\{1\right\}$
• D. $\left(\right.-\infty, \, -1\left.\right)\cup\left(\right.1, \, \infty\left.\right)$

Answer 1

Answer: (A)

$x^{2}-1\geq 0$
$\Rightarrow x^{2}\geq 1$
$\Rightarrow x\in \left(- \infty ​ , \, - 1\right]\cup\left[1 , \infty\right)\ldots \ldots .\left(\right.1\left.\right)$
and $x-1>0$
$\Rightarrow x>1$
$\Rightarrow x\in \left(1 , \, \infty\right)\ldots \ldots \left(2\right)$
From 1 and 2
$x\in \left(\right.1, \, \infty\left.\right)$