Answer
a) $(-1,0)\cup(1,\infty)$.
b) $(-\infty,-1]\cup[0,1]$.
Work Step by Step
As we can see on the graph:
a) $f(x)<0$ in the intervals $(-1,0)\cup(1,\infty)$ because the graph of the function is below the x-axis (which is $y=f(x)=0$) on these intervals. $0$ and $1$ are not inlucded because the inequality involves less than.
b) $f(x)\geq0$ in the intervals $(-\infty,-1]\cup[0,1]$ because the graph of the function is above or the x-axis (which is $y=f(x)=0$) on these intervals. $-1$, $0$ and $1$ are included because the inequality involves greater than or equal to.