When
f(x)=x^7+2x^3+x-1
I have found
f^-1(3)=1
But I need to prove this.
Can anyone help?
If finding is a 'categoric imperative' , then a method based on advanced tecniques of complex analysis will be supplied without demonstration...
If the function the inverse of which has to be found is...
(1)
... then first with the variable substitution we obtain...
(2)
Now the inverse of a function for which is can be written in series expansion as...
(3)
... where the are given by...
(4)
In our case of course is...
(5)
... and the x as function of y will be...
(6)
Details of computation of the are left to the [young I suppose...] starter of the thread...
Kind regards