Range of function $y=(e^x-e^{-x})/(e^x+e^{-x})$ What will be the range of function $y=(e^x-e^{-x})/(e^x+e^{-x})$ ? 
How should I approach this category of problems with exponential functions?  Please Help.

One way to analyze the possible values the given function can take on is to transform it into the "simplest possible" form.  Some arithmetic we might apply could look like this:
$$y=\frac{e^x-e^{-x}}{e^x+e^{-x}}\\
=\frac {e^{2x}-1}{e^{2x}+1}\\
=1-\frac 2{e^{2x}+1}$$
We could go further with this directly and fully invert the function, but we can immediately make some conclusions from where we are now:


*

*$e^{2x}+1\in(1,\infty)$

*$\frac 2{e^{2x}+1}\in(0,2)$


This leads us to $y\in(-1,1)$.
