Question

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

Answer 1

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}`