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Math Help - Ranges of a function

  1. #1
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    Ranges of a function

    If \pi \in (0,1), state the ranges of

    (a) log( \pi)

    (b) log( \pi/(1− \pi))

    (c) exp( \pi)/(1+exp( \pi))

    Anyone know how to find these?

    Thanks
    Last edited by mr fantastic; November 22nd 2010 at 11:09 PM.
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  2. #2
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    (a) (-\infty, 0] It may help to look at a graph

    (b) use properties of logs to break up this log

    (c) a graph may help here e^0=1 and e^1=e=2.71...
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  3. #3
    Senior Member BAdhi's Avatar
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    for (c) can't you follow the following method

    \frac{e^\pi}{e^\pi+1} = \frac{e^\pi+1-1}{e^\pi+1}

        =1-\frac{1}{e^\pi+1}

    e^0<e^\pi<e^1

    2<e^\pi+1<e+1

    0.5>\frac{1}{e^\pi+1}>\frac{1}{e+1}

    0.5<1-\frac{1}{e^\pi+1}<1-\frac{1}{e+1}<br />

    R(f)=(0.5,(1-\frac{1}{e+1}))

    (if f is the function)
    am I correct?
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