Question

The domain of definition of the function $y=\frac{325}{197}\left[\frac{\sqrt{x^2-1}}{\sqrt{x-1}}\right]$

• A. $(1,\infty )$
• B. $[1,\infty )$
• C. Set of all real numbers
• D. $(-\infty ,-1)\cup (1,\infty )$

Answer 1

The correct option is A $(1,\infty )$

$y=\frac{325}{197}\left[\frac{\sqrt{x^2-1}}{\sqrt{x-1}}\right]$

$\text{For y to be defined,}$

$\sqrt{x-1}\ne 0$

$x\ne 1$

$x\in R-\left\{1\right\}-\left(i\right)$

$x-1>0$

$x>1$

$x\in (1,\infty )-\left(ii\right)$

$x^2-1>0$

$x^2>1$

$x\in (-\infty ,-1)\cup (1,\infty )-\left(iii\right)$

All above the conditions must satisfy

$x\in (1,\infty )$