Inverse Trigonometric Functions Question 73
Question: The range of $ f(x)=si{n^{-1}}x+{{\tan }^{-1}}x+{{\sec }^{-1}}x $ is
Options:
A) $ ( \frac{\pi }{4},\frac{3\pi }{4} ) $
B) $ [ \frac{\pi }{4},\frac{3\pi }{4} ] $
C) $ { \frac{\pi }{4},\frac{3\pi }{4} } $
D) None of these
Show Answer
Answer:
Correct Answer: C
$ f(x)=si{n^{-1}}x+{{\tan }^{-1}}x+{{\sec }^{-1}}x; $
clearly, the domain of $ f(x) $ is $ x \neq \pm 1. $
Thus the range is $ {f(1),f(-1)},\text{i.e.},{ \frac{\pi }{4},\frac{3\pi }{4} }. $
BETA
