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).

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The Answer of 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).

Let f(x)=tan⁡−1x+tan⁡−11xf ( x ) = \tan ^ { - 1 } x + \tan ^ { - 1 } \frac { 1 } { x }f(x)=tan−1x+tan−1x1​

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