Dr Finlay Posted October 18, 2005 Share Posted October 18, 2005 Would the inverse function of [math] \displaystyle\frac{1 + e^x}{1 - e^x}[/math] be [math]\displaystyle\frac{e^x - 1}{e^x + 1}[/math] ? Just been working through Stewarts calculus, the book only gives answers to the odd numbered questions. Most of the concepts in the book are pretty new to me, having only just started my Alevels, so i thought it would be best to get as much practice at it as i could. Cheers, Rob Link to comment Share on other sites More sharing options...
Ducky Havok Posted October 18, 2005 Share Posted October 18, 2005 No, that is not the inverse. I believe all you did was say 1 over the function, right? The way to do inverses is to switch your x's and y's in the equation, and the solve for y. [math]x=\frac{1+e^y}{1-e^y} [/math] [math]x-xe^y=1+e^y[/math] [math]x-1=(x+1)e^y[/math] [math]\frac{x-1}{x+1}=e^y[/math] [math]\ln{\frac{x-1}{x+2}}=y[/math] or [math]\ln{(x-1)}-\ln{(x+2)}=y [/math] Link to comment Share on other sites More sharing options...
Dr Finlay Posted October 19, 2005 Author Share Posted October 19, 2005 Cheers mate Link to comment Share on other sites More sharing options...
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