The range of $$f\left( x \right) = {\sin ^{ - 1}}x + {\tan ^{ - 1}}x + {\sec ^{ - 1}}x$$       is

Solution :
$$f\left( x \right) = {\sin ^{ - 1}}x + {\tan ^{ - 1}}x + {\sec ^{ - 1}}x;$$       clearly, the domain of $$f\left( x \right)$$  is $$x = \pm 1.$$   Thus the range is $$\left\{ {f\left( 1 \right),f\left( { - 1} \right)} \right\}{\text{, i}}{\text{.e}}{\text{., }}\left\{ {\frac{\pi }{4},\frac{{3\pi }}{4}} \right\}.$$