From f(x) = √(mx) ; if x is posive m has to be positive; if x is negative m has to be negative; if x is cero m can have any value, and the range will always be 0 or positve
From g(x) = m √x; x can only be 0 or positive and the range will have the sign of m.
Given we concluded that the range of f(x) can only be 0 or positive, then me can only be 0 or positive.