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How can we find the inverse of this function? $$y=\exp(ax)+\exp(bx),$$ where $a$ and $b$ are constants

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Why did you use maple tag? –  B. S. Dec 7 '12 at 11:58
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Another useful link math.stackexchange.com/q/23705/8581. –  B. S. Dec 7 '12 at 12:01
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In general, there is no closed form for it. For example, if $a=5$, $b=1$, write $t=e^x$, then you have $t^5+t-y=0$, and it's well-known you can't solve for $t$ in terms of elementary functions.

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