# Thread: continuety prove question..

1. ## continuety prove question..

prove that if f(x) and g(x) are continues
so are those:
http://img508.imageshack.us/img508/1639/64747667bx8.gif

??

2. Originally Posted by transgalactic
prove that if f(x) and g(x) are continues
so are those:
http://img508.imageshack.us/img508/1639/64747667bx8.gif

??
Hint: Consider writing $\varphi(x)=\max\left\{f(x),g(x)\right\}$ as a piecewise function where the splits occur where the max changes from being $\varphi(x)=f(x)$ to $\varphi(x)=g(x)$.

For example consider the function $\varphi(x)=\max\left\{x,2x-1\right\}$ on the interval $[0,2]$. It is clear that $\varphi(x)$ may be written as $\varphi(x)=\left\{ \begin{array}{rcl} x & \mbox{if} & 0\leqslant x \leqslant 1\\
2x-1 & \mbox{if} & 1

3. Hint: $\max (f,g) = \tfrac{1}{2}(f+g) + \tfrac{1}{2}|f-g|$

4. ok i see that in a case of f>g it will return f
if f<g it will return g

but can i use your expression as a given??