anonymous 5 years ago prove that [1 - e^(1/x)]/ [1+ e^(1/x)] is odd.

1. anonymous

replace x by -x and see that you get the same thing back. would you like me to work out the gory detail?

2. anonymous

please if you could thatd be great

3. anonymous

$f(x)=\frac{1-e^{\frac{1}{x}}}{1+e^{\frac{1}{x}}}$ $f(-x)=\frac{1-e^{-\frac{1}{x}}}{1+e^{-\frac{1}{x}}}$ multiply top and bottom by $e^{\frac{1}{x}}$ to get $f(-x)=\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}=-\frac{1-e^{\frac{1}{x}}}{1+e^{\frac{1}{x}}}$ so $f(-x)=-f(x)$ and it is odd

4. anonymous

if any step is not clear let me know.

5. anonymous

thnxs a lot

6. anonymous

welcome