What is the domain and range of ## y= sqrt(x) -2##?

##"Domain="RR^=uu{0}=[0,oo).##

##"Range="[-2,oo).##

We will restrict our discussion in ##RR.##

As we can not find the square root of ##x<0, x>=0##

So, the Domain is the set of all non-negative reals, i.e.,

##RR^+uu{0}=[0,oo).##

Also, ##AA x in RR^+uu{0}, sqrtx>=0 rArr y=sqrtx-2>=-2.##

Hence, the Range is ##[-2,oo).##

Enjoy maths.!