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What is the domain of the function $\ell$ where $\ell(x)=\frac{2}{x-3}\text{,}$ using interval notation?

If needed, use inf for $\infty$ and U for $\cup\text{.}$

Solution

The function $\ell$ cannot take a $3$ as an input. It can, however, take any other number as input. Representing this on a number line, we have an interval $(-\infty,3)$ to the left of $3\text{,}$ and $(3,\infty)$ to the right of $3\text{.}$ So we find the domain is $(-\infty,3)\cup(3,\infty)\text{.}$