# Proving the Continuous Function

• December 26th 2010, 05:43 AM
ZOOZ
Proving the Continuous Function
be the Function (in the picture)

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

thanks.
• December 26th 2010, 06:06 AM
Plato
How rigorous must the proof be?
What theorems can be used?
• December 27th 2010, 03:21 AM
HallsofIvy
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.
• December 28th 2010, 02:24 AM
ZOOZ
thanks from here i know how to keep.