Question

Domain of the function $f\left(x\right)=$ $\frac{x-3}{(x-1)\sqrt{x^2-4}}$

• A. $(1,2)$
• B. $(-\infty ,-2)\cup (2,\infty )$
• C. $(-\infty ,-2)\cup (1,\infty )$
• D. $(-x,x)-(t\pm 2)$

Answer 1

The correct option is B $(-\infty ,-2)\cup (2,\infty )$

Given,

$f\left(x\right)=\frac{x-3}{(x-1)\sqrt{x^2-4}}$

$\sqrt{f\left(x\right)}\Rightarrow f\left(x\right)\ge 0$

$x^2-4\ge 0:x\le -2orx\ge 2$

Undefined singularity points $x<-2orx>2$

Domain $x<-2orx>2$

So, the domain is $(-\infty ,-2)\cup (2,\infty )$