# How do you find the domain and range of x + sqrt( x-1 )?

May 27, 2017

See below.

#### Explanation:

Since a square root cannot have a negative under the radical (or else it would be imaginary),

$x \setminus \ge q 1$.

When $x = 1$, the range (or $y$) is $\left(1\right) + \sqrt{1 - 1} = 1$. Thus, the range of $y$ is $y \ge q 1$

Thus, in interval notation, the domain of the function is $\left[1 , \infty\right)$, and the range is $\left[1 , \infty\right)$