Q19 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

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

Correct answer
A
$(1, \infty)$
B
$[1, \infty)$
C
$R - \{1\}$
D
$(- \infty, - 1) \cup (1, \infty)$

Solution

x^{2} - 1 \geq 0

\Rightarrow x^{2} \geq 1

\Rightarrow x \in (- ∞​, - 1] \cup [1, \infty) \dots \dots . (1)

and

x - 1 > 0

\Rightarrow x > 1

\Rightarrow x \in (1, \infty) \dots \dots (2)

From 1 and 2

x \in (1, \infty)

Hence, the correct answer is option: 'A'.

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