What is the domain and range of # f(x) = x / (3x(x-1))#?
In order to determine the domain, we need to see which part of the function restricts the domain. In a fraction, it is the denominator. In a square root function, it is what's inside the square root.
Hence, in our case, it is
In a fraction, the denominator can never be equal to 0 (which is why the denominator is the restricting part of the function).
So, we set:
The above means that:
Which gives us:
Thus, the domain of the function is all real numbers, EXCEPT
In order words, domain f(x):