# What is the domain and range of # f(x) = x / (3x(x-1))#?

##### 1 Answer

Jan 13, 2018

Domain f(x):

#### Explanation:

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):