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

1 Answer
Jan 13, 2018

Domain f(x): {x epsilon RR | x != 0, 1}

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 3x(x-1).

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:
3x(x-1) != 0

The above means that:
3x!= 0 AND (x-1) !=0

Which gives us:
x !=0 AND x !=1

Thus, the domain of the function is all real numbers, EXCEPT x = 0 and x = 1.

In order words, domain f(x): {x epsilon RR | x != 0, 1}