Mathematics

The key is to recognize that the floor function and absolute value behave differently on different intervals, so you'll need to split the domain into cases. On any interval $[n, n+1)$ where $n$ is an integer, $\lfloor x \rfloor$ is constant, but $|x|$ changes its form at $x=0$. By carefully evaluating $f$ on each relevant piece, you'll see a piecewise pattern emerge that makes the evaluation straightforward.

The key is to recognize that the floor function and absolute value behave differently on different intervals, so you'll need to split the domain into cases. On any interval $[n, n+1)$ where $n$ is an integer, $\lfloor x \rfloor$ is constant, but $|x|$ changes its form at $x=0$. By carefully evaluating $f$ on each relevant piece, you'll see a piecewise pattern emerge that makes the evaluation straightforward.