A) \[\left( \frac{\pi }{4},\frac{3\pi }{4} \right)\]
B) \[\left[ \frac{\pi }{4},\frac{3\pi }{4} \right]\]
C) \[\left\{ \frac{\pi }{4},\frac{3\pi }{4} \right\}\]
D) None of these
Correct Answer: C
Solution :
[c] \[f(x)=si{{n}^{-1}}x+{{\tan }^{-1}}x+{{\sec }^{-1}}x;\]clearly, the domain of \[f(x)\] is \[x=\pm 1.\] Thus the range is \[\{f(1),f(-1)\},i.e.,\left\{ \frac{\pi }{4},\frac{3\pi }{4} \right\}.\]
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