Let $f ( x ) = \tan ^ { - 1 } x + \tan ^ { - 1 } \frac { 1 } { x }$

Essay

Let $f ( x ) = \tan ^ { - 1 } x + \tan ^ { - 1 } \frac { 1 } { x }$ .(a) Show that $f ( x )$ is constant on $( - \infty , 0 ) \text { and } ( 0 , \infty )$ .(b) Determine the value of the constant(s).