A) \[\left\{ x:\frac{\pi }{4}+2n\,\pi \le x\le \frac{3\pi }{4}+2n\pi ;n\in l \right\}\]
B) \[\left\{ x:\frac{5\pi }{4}+2n\,\pi \le x\le \frac{7\pi }{4}+2n\,\pi ;n\in l \right\}\]
C) \[\left\{ x:\frac{\pi }{4}+2n\,\pi \le x\le \frac{3\pi }{4}+2n\,\pi \right\}\cup \]\[\left\{ x:\frac{5\pi }{4}+2n\,\pi \le x\le \frac{7\pi }{4}+2n\,\pi \right\}\]
D) None of the above
Correct Answer: C
Solution :
The given function \[f(x)=\sqrt{\frac{1}{2}-{{\cos }^{2}}x}\]is continuous at all the points where\[\frac{1}{2}-{{\cos }^{2}}x\ge 0\] \[\Rightarrow \]\[|\cos x|\le \frac{1}{\sqrt{2}}\]\[\Rightarrow \]\[\frac{\pi }{4}+2n\,\pi \le x\le \frac{3\pi }{4}+2n\pi \] or\[\frac{5\pi }{4}+2n\,\pi \le x\le \frac{7\pi }{4}+2n\,\pi ,n\in l\]
You need to login to perform this action.
You will be redirected in
3 sec
