anonymous
  • anonymous
prove that [1 - e^(1/x)]/ [1+ e^(1/x)] is odd.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
replace x by -x and see that you get the same thing back. would you like me to work out the gory detail?
anonymous
  • anonymous
please if you could thatd be great
anonymous
  • 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

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anonymous
  • anonymous
if any step is not clear let me know.
anonymous
  • anonymous
thnxs a lot
anonymous
  • anonymous
welcome

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