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domain/range

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Domain of the function ƒ(x) is the set of values of "x" or "input" for which the function is defined.
Range of the function ƒ(x) = y is the values of "y" or output"
In set of real numbers √a is the real number if a ≥ 0

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Domain (possible value of "x")
ƒ(x) = √(x - 3) is defined in set of real numbers if (x - 3) ≥ 0
              x - 3 ≥ 0
              x ≥ 3   or  [3, +∞)  
Range (possible value of "y"):  
The minimum value of given function:  ƒ(3) = 0
             y = ƒ(x) ≥ 0  or  [0, +∞)  

the domain is x≥3 and the range is y≥0

x-3≥0  =  x≥3 (by adding three to both sides) = Domain 

For range, y can be any number greater than 0, because when y=0 x=3 = Range 

 

You can check this also by entering the equation in a calculator