Question

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

Answer 1

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

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

Explanation:

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.!