$f(x) = [x] + [-x]$ for $x \ne 2$, and the value of $f$ at $x = 2$ is $k$. For which $k$ is $f$ continuous at $x = 2$?

Explanation

1. 01

   Just left of 2: $[x] = 1$ and $[-x] = -2$, sum $-1$. Just right of 2: $[x] = 2$ and $[-x] = -3$, sum $-1$.

2. 02

   Both one-sided limits are $-1$, so $k = -1$.