Question

How do I find the domain of the function in this problem?
f(x)=x/3x-1

Answer 1

The domain required, if we're talking about only real numbers here, is when imputing an x into the denominator to make the denominator NOT 0. Therefore, the domain is when \[x \neq 1/3\]

Answer 2

Now what about the infinite union?

Answer 3

Now what about the infinite union?
If your function is \[ f(x)=\frac{x}{3x-1} \] the domain is exactly \[x\neq \frac{1}{3}\]. Representing this as a union would be: \[(-\infty , \frac{1}{3}) \cup (\frac{1}{3}, \infty \]

Answer 4

I forgot to close the parenthesis:

\[(-\infty, \frac{1}{3}) \cup (\frac{1}{3}, \infty)\]