Answer
a. {$x$|$x$ is a real number, $x\ne0$}
b. $(-∞,0)U(0,∞)$
Work Step by Step
We are given the function $f(x)=\frac{12x+3}{x}$. The domain of the function will be all values of $x$ such that the denominator does not equal 0.
Therefore, we can set the denominator equal to 0. We will exclude from the domain all values of $x$ that make the denominator equal 0.
$x=0$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne0$} in set-builder notation and $(-∞,0)U(0,∞)$ in interval notation.