Independence of function from an input variable

Hi I’m wondering if there is a way to check if a function is independent from one of its input variables. For example, if we consider the function f(x,μ) = x, I’m looking for a method that tells me that the function μ -> f(x,μ) is constant. In addition, μ is a continuous variable, so checking that f is constant for all values of μ, for a fixed x, is impossible. Thank you in advance!