Try this explanation:
1) Domain of the given function.
to define the domain of the function: sqrt(x)≥0, ⇒ x≥0.
It means, the domain is x∈[0;+∝).
2) Range of the given function.
Property of this function: when the 'x' is the minimum value, then the 'g(x)' has minimum value; when the 'x' is the maximum value, then the 'g(x)' has maximum value. Using this property and the domain defined above, minimum of g(x) is 3 (the expression has '+3'!), maximum is +∝.
It means, the range is g(x)∈[3;+∝).
