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Thread: Ranges of a function

  1. #1
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    Ranges of a function

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

    (a) log($\displaystyle \pi$)

    (b) log($\displaystyle \pi$/(1−$\displaystyle \pi$))

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

    Anyone know how to find these?

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

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

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

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

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

    $\displaystyle e^0<e^\pi<e^1$

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

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

    $\displaystyle 0.5<1-\frac{1}{e^\pi+1}<1-\frac{1}{e+1}
    $

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

    (if $\displaystyle f$ is the function)
    am I correct?
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