# Math Help - Proving the Continuous Function

1. ## Proving the Continuous Function

be the Function (in the picture)

how i Prove that the functionare Continuous for any x>or=0 ?

thanks.

2. How rigorous must the proof be?
What theorems can be used?

3. An "epsilon-delta" proof would be long and tedious. A proof using the facts that $\sqrt{x}$, $2x$, and $tan^{-1}(x)$ are continous functions and that the composition of continuous functions is continuous would be almost trivial.

4. thanks from here i know how to keep.