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Q.
The range of the function $f(x)=\sec ^{-1}(x)+\tan ^{-1}(x)$, is
Inverse Trigonometric Functions
Solution:
$D _{ f }=(-\infty,-1] \cup[1, \infty)$
Also, $f$ is an increasing function.
For, $x \in(-\infty,-1], f(x) \in\left(0, \frac{3 \pi}{4}\right]$......(1)
and for $x \in[1, \infty), f(x) \in\left[\frac{\pi}{4}, \pi\right)$.....(2)
$\therefore$ For range of $f ( x ),(1) \cup(2) \Rightarrow(0, \pi)$.