I have the following function: $$ g_{n}(x) = \frac{x^n}{1+x^n} $$ with $$ g_{n}:D_{n} \rightarrow \mathbb{R} $$
I want to define the maximal definition range of $ D_{n} \subset \mathbb{R} $ and check where the function g is continuous, but have some trouble coming up with the right answer for this one.
For the first problem, is it correct to assume that the denominator of the function has to be zero? Thus I need to solve the following equation? $$ 1+x^n = 0 $$
As for the second problem I have no clue as to how I should approach this, since I am facing a function with two variables. Any clues are appreciated!