I need help with finding out the domain of f(x)= sqrt(x(x-2)). I keep getting the wrong answer. Please help me out and explain.

Answer 1

You know that you cannot take the square root of a negative number. That means that you must have

x(x-2) >= 0
So, either both factors are negative, or both are positive. Thus, the domain is (-∞0]U[2,∞)

You can visualize this by graphing the parabola. It opens upward, so it is negative between the roots (0,2) and positive outside that interval.