Maybe I'm getting a bit ahead of myself here, but for the sake of curiosity I'll ask it anyways. Is there any way that you can test when a function h(x) will have transcendental outputs vs rational or algebraic outputs? Specifically, if I have the following function f(x) = ssrt(x) Where ssrt is the inverse of a second degree power tower (ssrt(x^x) = x). Meaning, for a given value of x, the ssrt() function will give me the number that when raised to the power of itself equals x. Good examples of this function are ssrt(4) = 2 because 2^2 = 4 and ssrt(27) = 3 because 3^3 = 27. Would it be possible to find the x intervals that make f(x) transcendental?