That website

http://wims.unice.fr contains a plenty of useful online calculators,

really a lot, but I couldn't find out a place where inverse of functions is being sought.

For example take up with 1.

Can put with

and then solve with that quadratic for

.

The inverse is being given by

2.

The inverse of this function is given by

just simply this case goes away within that way.
3.

Writing with this function as

The inverse can be given by

OK, then what will be the inverses of these following functions?

It seems that they cannot be solved by using all those elementary mathematical functions at all!

(4)

(5)

(6)

(7)

(8)

(9) e

(10)

Thanks for your help, if possible within any case

Disclaimer:

I had faced a problem which asked me to give an algorithm to check out if N is a perfect power, x

^{y} where that value of y is ≥ 2. I told that it can be done by using checks of

,

,

,

,

,

, ... alternately, what value to check upto for base? Till N = z

^{z}, for some value of z. Thus, how to write up with that value of z as a function of N?

How does that way work out rather...