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

Oct 13, 2017

You can get the domain by working with the assumption that the function's domain lie in a set of all real numbers, that is $\left(x - 1\right)$ must be greater than or equal to zero.

#### Explanation:

If $\left(x - 1\right)$ must be greater than $0$ then $x \ge 1$ must be true for all values of $x$.

Therefore the domain is $x \ge 1$

The range is suppose to be the set of all values of the function that lies within the domain.
The least member of the domain set above is $x = 1$ and the value of the function at this value of $x$ is √1 which is $1$.
Therefore the range is $\left\{1 , \ldots\right\}$