Explanation:
[tex]f(x)=\frac{3x}{x-1}[/tex]To find the domain we have to take a look at every part of the function that contains 'x'. In this function there are two places where x is:
[tex]3x\rightarrow\text{ there's no restriction about the values 'x' can take in this part}[/tex][tex]\begin{gathered} (x-1)\rightarrow\text{ since this is in the denominator of the function, it cannot be zero} \\ \text{therefore} \\ x-1\ne0\Rightarrow x\ne1 \end{gathered}[/tex]Answer:
The domain of the function is all real numbers except 1:
[tex]D\colon x\in(-\infty,1)\cup(1,\infty)[/tex]Around x = 1, the function goes to infinty. To the left of x = 1 it's negative infinity and to the right it's positive infinity
