Let $f(x)=[x]\sin\left(\frac{π}{[x+1]}\right)$, where [x] denotes the greatest integer function. Then domain of f is
Answer & explanation
Correct answer: option 3
For $D_f : [x +1] ≠ 0$
But $[x + 1]=0⇔0≤x+1<1⇔-1≤x<0$
$∴D_f=R-[-1,0)=(-∞, -1)∪[0, ∞)$
Let $f(x)=[x]\sin\left(\frac{π}{[x+1]}\right)$, where [x] denotes the greatest integer function. Then domain of f is
Correct answer: option 3
For $D_f : [x +1] ≠ 0$
But $[x + 1]=0⇔0≤x+1<1⇔-1≤x<0$
$∴D_f=R-[-1,0)=(-∞, -1)∪[0, ∞)$