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Thread: continuity

  1. #1
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    Question continuity

    If f is a function on [0,1] for which f '(1/2) existsbut f '(1/2) does not belong to [0,1], then f is discontinous at x=1/2. State true or false .Giver reason?
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  2. #2
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    Quote Originally Posted by puneet View Post
    If f is a function on [0,1] for which f '(1/2) existsbut f '(1/2) does not belong to [0,1], then f is discontinous at x=1/2. State true or false .Giver reason?
    Well as stated there is no problem as $\displaystyle f(x)=100x$ will do as our function.

    So lets suppose $\displaystyle f:[0,1] \leftarrow [0,1] $, well then:

    $\displaystyle
    f(x) = \left\{ {\begin{array}{ll}
    0, & {x < 1/4} \\
    {2x - 1/2}, & {1/4 \le x < 3/4} \\
    1, & {3/4 \le x} \\
    \end{array}} \right.
    $

    RonL
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