Question

The domain of definition of the function $f\left(x\right)=\frac{\sqrt{si{n}^{-1}x+\sqrt{(x^2+1)}}+\sqrt{x-\left[x\right]+lnx}}{e^{\sqrt{(sinx+cosx)}}+ln\left(sin\left(\frac{1}{\sqrt{-x^2}}\right)\right)}$ (where [.] denotes the greatest integer function)

• A. $(1,1)$
• B. $(0,1)$
• C. $(1,0)$
• D. None of these

Answer 1

The correct option is D None of these

In the denominator of $f\left(x\right)$ , In the term $sin\left(\frac{1}{\sqrt{-x^2}}\right)$

$-x^2$ should be $\ge 0$ for $\sqrt{-x^2}$ to exist

$\Rightarrow x^2\le 0$

$\Rightarrow x=0$

But for $x=0$ , the sine term doesnt exist

Therefore the correct option is $D$