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## Main Question or Discussion Point

Let,s suppose we want to obtain the inverse of the functions:

[tex] y=\frac{sin(x)}{x} [/tex] [tex] y=cos(x)+x [/tex] or [tex] y=\int_{c}^{x}dt/logt [/tex]

as you can check you can,t explicitly get g(y)=x from y=f(x)..then how would you manage to get it?..i have heard about Lagrange inverse series theorem to invert a series..but what happens if the function is not analytic on the whole real line?..for example includes terms in the form |x|, lnx, 1/x or x^{r} with r a real number.

[tex] y=\frac{sin(x)}{x} [/tex] [tex] y=cos(x)+x [/tex] or [tex] y=\int_{c}^{x}dt/logt [/tex]

as you can check you can,t explicitly get g(y)=x from y=f(x)..then how would you manage to get it?..i have heard about Lagrange inverse series theorem to invert a series..but what happens if the function is not analytic on the whole real line?..for example includes terms in the form |x|, lnx, 1/x or x^{r} with r a real number.