## Finding a Taylor Series About a Point for an inverse Function

Given a Taylor series about a pointfor a functionwhereandwe can find the Taylor series aboutforby puttingand equating powers ofin the identityto obtain equations foretc in terms ofSince we know thewe can evaluate the

Example: Obtain the Taylor series for the inverse ofabout

The Taylor series foraboutis

whereandsatisfy

Equating coefficients of powers of z- %apha =z we obtain

Then

Since labels are arbitrary, we can write