Question

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

• A. All real numbers except for $0$
• B. All real numbers greater than or equal to $1$
• C. All real numbers less than or equal to $1$
• D. All real numbers greater than or equal to $-1$ but less than or equal to $1$
• E. All real numbers less than or equal to $-1$

Answer 1

The correct option is B All real numbers greater than or equal to $1$

$f\left(x\right)=\frac{\sqrt{x-1}}{x}$, for $f\left(x\right)$ to exist, the expression in the square root must be non - negative and the expression in denominator should not be equal to $0$.
So, $x-1\ge 0$ and $x\ne 0$
$x\ge 1$ and $x\ne 0$, which implies $x\ge 1$.