# Thread: Ranges of a function

1. ## 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

2. (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 $e^1=e=2.71...$

3. 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

$2

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

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

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

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