Answer
a. {$x$|$x$ is a real number, $x\ne-3$}
b. $(-∞,-3)U(-3,∞)$
Work Step by Step
We are given the function $f(x)=\frac{x}{x+3}$. 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.
$x+3=0$
Subtract 3 from both sides.
$x=-3$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne-3$} in set-builder notation and $(-∞,-3)U(-3,∞)$ in interval notation.