Suppose that I have a function:
$f(x,U) = x + \log(U)$
where $x$ and $U$ can be complex numbers. I take $f(x,U)$ and evaluate it a number of times for different $x$ and $U$.
Since $U$ can be complex, I take $\log(U)$ as the complex logarithm (Wikipedia Link). For example, $\log(-1) = 3.1416i$.
Now suppose that for all of my function evaluations, $x = 0$ so:
But given only $f(x,U)$, and not knowing $x$ and $U$, is there a way to use curve-fitting or some other method to determine that $f(x,U) = \log(U)$ and $x = 0$?
Can numerical methods be used to distinguish between $f(x,U) = x + \log(U)$ and $f(x=0,U) =\log(U)$, and how would I deal with the real and complex parts?
I assume that $\log(U) \neq 0$ for all function evaluations, and that $x \neq \log(P)$, where $P$ is some complex number.
I've found a similar question on Stack Overflow (link), but I am uncertain as to whether something from that question can be used to solve this problem.
Is this problem less of an issue when considered with the complex set of numbers in lieu of the reals?