1. The problem statement, all variables and given/known data Hello! Seems I have forgotten how to work with such values. Please, help me to find the correct approach to this type of exercises. 2. Relevant equations The task is to find the domain of the function: f(x) = arccsc(e2x) 3. The attempt at a solution The answer in the book is [0, ∞). The domain of arccsc(x) is (-∞, -1] U [1, ∞) (1) In the given function x is an exponent of epsilon, and also it has coefficient 2. So, I see that I need to divide by 2. (2) So, if x = -1, then the exponent will be -½, and thus it would mean that I need to take "a negative square root" of e. This means that I have to discard this option, and thus discard all negative values, and concentrate only on [1, ∞) part. (3) If x = 1, then exponent will be ½, meaning I need to take the square root of e. I don't see my next steps. Logically it does look as if all values starting from 0 and till ∞ are correct, because all can be e's exponent, but how to get there mathematically? Thank you very much!