Question

3.2 Find the domain of f (x)= 3x/x-1 and discuss the function behavior of f near any excluded x-values.

Answer 1

Step-by-step explanation:

`f(x)=(3x)/(x-1)`

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:

`3x\rightarrow\text{ there's no restriction about the values 'x' can take in this part}`
`\begin{gathered} (x-1)\rightarrow\text{ since this is in the denominator of the function, it cannot be zero} \\ \text{therefore} \\ x-1\\e0\Rightarrow x\\e1 \end{gathered}`

Answer:

The domain of the function is all real numbers except 1:

`D\colon x\in(-\infty,1)\cup(1,\infty)`

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