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

Mathematics
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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 \[x \neq 1/3\]
Now what about the infinite union?

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Other answers:

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: \[(-\infty , \frac{1}{3}) \cup (\frac{1}{3}, \infty \]
I forgot to close the parenthesis: \[(-\infty, \frac{1}{3}) \cup (\frac{1}{3}, \infty)\]

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