Question

The domain of $f\left(x\right)=\frac{\tan \pi \left[x\right]}{1+\sin \pi \left[x\right]+\left[x^2\right]}$ is (where [.] denotes greatest integer function)

• A. $(0,\infty )$
• B. $R$
• C. $(-\infty ,0)$
• D. $Z$

Answer 1

The correct option is B $R$

We know,
$\tan \left(\text{integral multiple of}\pi \right)=0,\sin \left(\text{integral multiple of}\pi \right)=0,\left[x^2\right]\ge 0$
Hence $f\left(x\right)=\frac{0}{1+0+(\text{some real number}\ge 0)}=0$
Therefore the domain of f is all real numbers i.e. $R$