# What is the domain of f(x)=sqrt(x-1)?

Sep 9, 2015

Domain: $\left[1 , + \infty\right)$

#### Explanation:

The domain of the function will be restricted by the fact that the expression under the square root cannot be negative for real number solutions.

This means that you need to have

$x - 1 \ge 0$

$x \ge 1$

Any value of $x$ that is smaller than $1$ will make the expression under the square root negative, which is why the domain of the function will be $\left[1 , + \infty\right)$.

graph{sqrt(x-1) [-7.9, 7.9, -3.95, 3.95]}