# What is the domain and range of F(x)=sqrtx ?

Jan 20, 2016

It depends. The domain is in a sense user-defined.

#### Explanation:

Whoever who created this function chooses his own domain.

For example, if I made this function, I could define its domain to be $\left[4 , 9\right]$. In that case, the corresponding range would be $\left[2 , 3\right]$.

But what I think you are asking for is the largest possible domain of $F$. Any domain of $F$ must be a subset of the largest possible domain.

The largest possible domain for $F$ is $\left[0 , \infty\right)$.
The corresponding range is $\left[0 , \infty\right)$.