Question

What is the domain of `f(x) = (3x-1) / (x^2-x)`?

Answer 1

Domain: `(-oo, 0) uu (0, 1) uu (1, + oo)`

Explanation:

Right from the start, you know that the domain of the function must not include any value of `x` that will make the denominator of the fraction equal to zero.

So basically, any value of `x` for which

`x^2 - x != 0`

wil be excluded from the function's domain.

You can rewrite this equation like this

`x^2 - x = 0`

`x * (x-1) = 0 implies {(x=0), (x=1) :}`

This means that the domain of the function will be `RR-{0, 1}`, or, in interval notation, `(-oo, 0) uu (0, 1) uu (1, + oo)`.

graph{(3x - 1)/(x^2 - x) [-46.22, 46.22, -23.1, 23.15]}