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. $(-\infty ,-1)\cup (1,\infty )$

Answer 1

Answer: (A)

$x^2-1\ge 0$
$\Rightarrow x^2\ge 1$
$\Rightarrow x\in \left(-\infty ,-1\right]\cup \left[1,\infty \right)\dots \dots .(1)$
and $x-1>0$
$\Rightarrow x>1$
$\Rightarrow x\in \left(1,\infty \right)\dots \dots \left(2\right)$
From 1 and 2
$x\in (1,\infty )$