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inverse function computation


Hello,

I'd like to do the following manipulation.
Let f be a homeomorphism (known explicitly).
I want Mathematica to compute its inverse f^{-1} and to use it
for further computations and plots.
I'm assuming here that f^{-1} is not explicit (take f(x)=x+0.2Sin[x] for
instance).

I'm not sure that Mathematica has an already built-in function; do you know
any simple algorithm?

Many thanks




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