Question

Let $f\left(x\right)=\sqrt{\left[\sin 2x\right]-\left[\cos 2x\right]}$, (where [.] denotes greatest integer function ) then range of $f\left(x\right)$ will be

• A. $\left\{0\right\}$
• B. $\left\{1\right\}$
• C. $\{0,1\}$
• D. $\{0,1,\sqrt{2}\}$

Answer 1

The correct option is A $\left\{0\right\}$

$\begin{array}{c}\sin xand\cos x=-1\left[\because Rangeof\sin \theta and\cos \theta is\left[-1,1\right]\right]\\ \Rightarrow f\left(x\right)=\sqrt{\left[-1\right]-\left[-1\right]}=\sqrt{-1+1}=0\\ Put\sin 2x=1,\left[\cos x\right]=\sqrt{\left[1\right]-\left[1\right]}=0\\ HenceRangeoffxis\left(0\right)\end{array}$