The intersection of the domains of functions: and
a)
b)
c)
d)
e)
Easiest is looking at the second function maybe.
For the expression under the square root sign to be positivt, we solve
So, this function makes boundaries
Looking at
That is,
The logharitm is defined for , so x>0
and arcsin(x) for .
So we get , giving us
when we combine the interval