#### Answer

a. {$x$|$x$ is a real number, $x\ne7$}
b. $(-∞,7)U(7,∞)$

#### Work Step by Step

We are given the function $f(x)=\frac{x}{x-7}$. 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.
$x-7=0$
Add 7 to both sides.
$x=7$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne7$} in set-builder notation and $(-∞,7)U(7,∞)$ in interval notation.