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How do you find an inverse function if that inverse can only be expressed as a Taylor series expansion?
For example, how do you find the inverse function of Y = X^X ? Solving for X in terms of Y can't be done using basic algebra. How do I calculate the power series expansion of the inverse function?
1 Answer
- AlanLv 71 month ago
A Taylor series doesn't help at all for the function
you mentioned.
Also, for even value of x between 0 and 1 , there are
two y values for every x so an inverse would not be a function.
so a Taylor series will be like the following
So with all different exponent levels. the Taylor
doesn't help find the inverse.
y = c + (x-a)*b + (x-a)^2*c + (x-a)^3*d + ...