Q. The largest possible set of real numbers which can be the domain of $f(x) = \sqrt{1 - \frac{1}{x}}$ is
A) $(0,\ 1) \cup (0,\ \infty)$
B) $( - 1,\ 0) \cup (1,\ \infty)$
C) $( - \infty,\ - 1) \cup (0,\ \infty)$
D) $( - \infty,\ 0) \cup \lbrack 1,\ \infty)$
Explanation
(d)
For $f(x)$ to be defined $\frac{x - 1}{x} \geq 0$
$\Rightarrow x \geq 1$ and $x < 0$
$\therefore$ Required interval is $( - \infty,\ 0) \cup \lbrack 1,\ \infty)$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.