Find the Domain of \(f(x)=\frac{3x-2}{x+1}\)
Question:
Find the domain of the following real valued function of real variable:
$$
f(x)=\frac{3x-2}{x+1}
$$
Solution
Given: $$ f(x)=\frac{3x-2}{x+1} $$
The denominator cannot be zero.
Therefore, $$ x+1\ne0 $$
$$ x\ne-1 $$
Hence, all real numbers except \(-1\) are allowed.
Therefore, the domain is: $$ \mathbb{R}-\{-1\} $$
or $$ (-\infty,-1)\cup(-1,\infty) $$