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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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    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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To verify or prove that $g(x)$ is the inverse of $f(x)$, you need to show that $g(f(x)) = f(g(x)) = x$.

That is, you show both $g(f(x)) = x$ and $f(g(x)) = x$.

If you can show this, then you can conclude $g(x) = f^{-1}(x)$. (Alternatively, and equivalently, you can conclude $f(x) = g^{-1}(x)$).

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If f(g(x)) = x and g(f(x)) = x, then you can say that f(x) is the g(x) inverse function.