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I think the easiest way is to calculate g(f(x)) or f(g(x)), but I don't know if it works in every case.

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    That's the definition, It does work when you can actually calculate :). A way to get a ballpark is to see if the graphs of $f$ and $g$ are a reflection of each other around the line $x=y$.2012-11-29
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    You could also try taking the equation $y = f(x)$ and solving it for $x$, which will end up giving you $g(y) = x$ if $g$ is the inverse of $f$.2012-11-29

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