Let $f(x)=[x]\sin\left(\frac{π}{[x+1]}\right)$, where [x] denotes the greatest integer function. Then domain of f is

(-∞, -1) [0, ∞) (-∞, -1)∪[0, ∞) none of these

(-∞, -1)∪[0, ∞)

For $D_f : [x +1] ≠ 0$ But $[x + 1]=0⇔0≤x+1<1⇔-1≤x<0$ $∴D_f=R-[-1,0)=(-∞, -1)∪[0, ∞)$