asymptotes for ln function

Hello! I am having trouble finding horizontal and vertical asymptotes for function

g(x)=ln(1-sqrt(1-x^2))

this is a derivative based assignment, is there a way to determine any of these elements with the derivative? (I know that the derivative is the rate of change so i don't see how this would help)

this is a calculus based question btw and i was wondering if i have to compute limits for this or use (analysis shown below).

I know that the domain is restricted to [-1,0)U(0,1], meaning that there is a vertical asymptote at x=0 and a horizontal asymptote I am assuming there are none.

Is there a method of solving this with limits or is it simply not required? Do I just need to analyze the question in that case?

thx in advance!