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Math Help - continuous function

  1. #1
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    continuous function

    I'm pretty sure this statement is false.
    Let f be a defined function. If abs(f) is continuous at a, then f is also continuous at a.

    Is this an accetable counterexample?
    f(x) =
    x + 1 if x does not equal zero
    1 if x equals zero.
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  2. #2
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    The function you have proposed is continuous everywhere.
    But you do have the right idea. Try this.
    f(x) = \left\{ {\begin{array}{rr}<br />
   { - 1} & {x < 0}  \\<br />
   1 & {0 \le x}  \\<br />
\end{array}} \right.
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  3. #3
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    Yeah I meant
    x + 1 if x does not equal zero
    -1 if x equals zero.
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  4. #4
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    Well yes. That will work also.
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