# How do you find the domain of f(x) = sqrt{(x - 1)/x + 4)?

The condition for f(x) to be defined and real is the quantity under the square root must be non-negative: $\frac{x - 1}{x} + 4 \ge 0$.
$\frac{x - 1}{x} + \frac{4 x}{x} = \frac{5 x - 1}{x} \ge 0$
$x$ not zero; and $\frac{5 x - 1}{x} > 0$.
So $x < 0$ or $x \ge \frac{1}{5}$
Domain of $f$: $\left(- \infty , 0\right) \cup \left[\frac{1}{5} , \infty\right)$