Inverse function

[Cogman]

So something I've been working on requires me to take the inverse of y=ln(x)*sqrt(x). I'm able to get it to y = e^(x/sqrt(y)) but can't seem to get that y out of the righthand side. Any tips from the math gurus here?

(I'm writing a program that has to take the sqrt of a number and multiply it by the log of the same function, I was trying to get the function ready to apply newtons method, but wound up at this halting point).

 

[Unitary]

Unfortunately, what you want to do is impossible. The function doesn't have an inverse on the domain x>0 because it is not one to one. Moreover, I think that even if you restrict the domain to where it does have an inverse (say x>1), it cannot be written in an elementary form (using roots logs polynomials ect.) anyway.

Best of luck with your project.

 

[Cogman]

Originally posted by: Unitary
Unfortunately, what you want to do is impossible. The function doesn't have an inverse on the domain x>0 because it is not one to one. Moreover, I think that even if you restrict the domain to where it does have an inverse (say x>1), it cannot be written in an elementary form (using roots logs polynomials ect.) anyway.

Best of luck with your project.

dang, that's somewhat what I feared. I guess I'll be better off then just taking the sqrt of the value and then multiplying that by the natural log of the value. Those inverses are at least easy I just wanted to eliminate a step or two by combining the multiplication step in the beginning.