I have a function given as $f(x^2)$ and the same function with some different variables $f(u^2)$, the constraint is both x and u are positive numbers. The function is given to be composed of square roots but nothing like floor or ceiling functions where the inversion of variable may lead to several different values in the domain. Can I then say that $$x=u$$ if $$f(x^2)=f(u^2)$$ Also, suppose now the function is given as $f(x^n)=f(u^n)$ where $n$ is positive integer, with the same constraints, then will $x=u$?
Also, If the condition $f(x^2)=f(u^2)$ does not guarntee equality what empirical/numerical methods I can use to check if both $x=u$, because plotting for different values will result in overlapping curves.
Any help will be highly appreciated.