Ranges of a function

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November 22nd 2010, 06:03 PM
sirellwood

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
November 22nd 2010, 06:06 PM
dwsmith

(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 $e^1=e=2.71...$
November 23rd 2010, 01:35 AM
BAdhi

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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