Question

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

Answer 1

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

Answer 2

please if you could thatd be great

Answer 3

\[f(x)=\frac{1-e^{\frac{1}{x}}}{1+e^{\frac{1}{x}}}\]
\[f(-x)=\frac{1-e^{-\frac{1}{x}}}{1+e^{-\frac{1}{x}}}\]
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

Answer 4

if any step is not clear let me know.

Answer 5

thnxs a lot

Answer 6

welcome