I'm agree for the domain, but why you say that the range are the reals? you actually know that , so the range must be between those values, and actually as you got the ln, you know that the range is
Thats how I see it.
We need to find the domain and range of (arctan(ln(sqrt(x)-1)))^3
I have domain and range of ln(sqrt(x)-1) as D: x>1 and R: reals. Is it correct? The arctan throws me off. I am not sure..I know for arctan(x), the domain is R and the range is (-pi/2,pi/2), but here I am not sure.