describe the domain and range of the equation f(x)=sqrt(x-2)-3

Question

please help me describe the domain and range of this equation f(x)=sqrt(x-2)-3

Answer 1

Given f(x) = Sqrt(x-2)-3

The domain of the function is set of all positive values for x .

The range is all possible values for y .

Here observe the function  here s squre root isinvolved.negtive squre root is not possible.

 Sqrt(x-2) ≥ 0 then x ≥ 2

So the domain is [2,∞]

Range is [-3,∞] since Sqrt(x-2) ≥ 0,f(x) ≥ -3