Question

The largest possible set of real numbers which can be the domain of $f\left(x\right)=\sqrt{1-\frac{1}{x}}$ is

• A. $(0,1)\cup (0,\infty )$
• B. $(-1,0)\cup (1,\infty )$
• C. $(-\infty ,-1)\cup (0,\infty )$
• D. $(-\infty ,0)\cup [1,\infty )$

Answer 1

The correct option is D

$(-\infty ,0)\cup [1,\infty )$

The explanation for the correct option.

Solve for the domain of $f\left(x\right)=\sqrt{1-\frac{1}{x}}$

$\frac{x-1}{x}\ge 0$

⇒$x\ge 1$and $x<0$

The domain is $(-\infty ,0)\cup [1,\infty )$

Hence, option(D) is the correct answer.