#### Answer

$$f(x)=\begin{cases}x+3, & x \lt 2 \\ x+3, & x \gt 2 \end{cases}$$
(Other answers are possible.)

#### Work Step by Step

Consider the function$$f(x)=\begin{cases}x+3, & x \lt 2 \\ x+3, & x \gt 2 \end{cases}.$$This function is not defined at $x=2$. Nonetheless, the limit at $x=2$ exists and equals:
$$\lim_{x \to 2}f(x)=5.$$
Please note that in the definition of the limit, $\lim_{x \to a}f(x)$, the function $f$ does not need to be defined at $x=a$.