1. **State the problem:** We need to evaluate the function $f(x) = \lfloor x \rfloor + \lfloor -x \rfloor$ at $a = 2$. 2. **Recall the floor function properties:** The floor function $\lfloor x \rfloor$ gives the greatest integer less than or equal to $x$. 3. **Evaluate each term:** - Calculate $\lfloor 2 \rfloor$: Since 2 is an integer, $\lfloor 2 \rfloor = 2$. - Calculate $\lfloor -2 \rfloor$: Since -2 is an integer, $\lfloor -2 \rfloor = -2$. 4. **Sum the results:** $$f(2) = \lfloor 2 \rfloor + \lfloor -2 \rfloor = 2 + (-2) = 0$$ 5. **Interpretation:** The function sums the floor of a number and the floor of its negative. For integers, this sum is always zero. **Final answer:** $$f(2) = 0$$