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Math Help - continuety prove question..

  1. #1
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    continuety prove question..

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

    ??
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by transgalactic View Post
    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\\<br />
2x-1 & \mbox{if} & 1<x\leqslant2 \end{array} \right.
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  3. #3
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    Hint: \max (f,g) = \tfrac{1}{2}(f+g) + \tfrac{1}{2}|f-g|
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  4. #4
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    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??
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