# Continuous Real Function/Examples/Root of x at 1

## Examples of Continuous Real Functions

Let $f: \R_{\ge 0} \to \R$ be the real function defined as:

$\map f x = \sqrt x$

Then $\map f x$ is continuous at $x = 1$.

## Proof

From Limit of Real Function: Example: $\sqrt x$ at $1$, we have that:

$\ds \lim_{x \mathop \to 1} \sqrt x = 1$

The result follows by definition of continuous real function.

$\blacksquare$