Answer
$f(1)=\displaystyle \frac{1}{3}$ makes the function continuous at $x=1$.
Work Step by Step
Graphing (see image below), and creating a table where values approach $x=a$ from either side, we see that $f(1)$ is undefined, but function values approach $\displaystyle \frac{1}{3}$, as $x$ approaches $a=1,$ both from the left and the right.
So, placing $f(1)=\displaystyle \frac{1}{3}$ makes the function continuous at $x=1$.
