Question

The domain of the function $f\left(x\right)=\sqrt{\frac{x^2-1}{x-2}}$ is

• A. $(2,\infty )$
• B. $(1,\infty )$
• C. $[-1,1]\cup (2,\infty )$
• D. none of these

Answer 1

The correct option is C $[-1,1]\cup (2,\infty )$

Given,

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

$\frac{x^2-1}{x-2}\ge 0:-1\le x\le 1orx>2$

undefined singularity point: $x=2$

combined domain of function,

$-1\le x\le 1orx>2$

$[-1,1]\cup (2,\infty )$