Find the domain of the functions given in the attached image.

1.
The first square root requiresbut if x=0 then the second term denominator goes to zero and hence the domain is


2.
The denominator must not be zero and the whole rational function must be positive
when x<0,|x| = -x and then if x<-1 then both numerator and denominator becomes neative and hence making the rational function positive, secondly for 1>x>=0 the denominator is positive which works too
Hence the domain is


3.
we deal with quadratic inside square roots
first one will give

|x| is always positive therefore what remains is

Now the second quadratic (taking the -ve)


taking the intersection of both the subdomains we get the domain as