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Let f(x)=tan1x+tan11xf ( x ) = \tan ^ { - 1 } x + \tan ^ { - 1 } \frac { 1 } { x }

question 198

Essay

Let f(x)=tan1x+tan11xf ( x ) = \tan ^ { - 1 } x + \tan ^ { - 1 } \frac { 1 } { x } .(a) Show that f(x)f ( x ) is constant on (,0) and (0,)( - \infty , 0 ) \text { and } ( 0 , \infty ) .(b) Determine the value of the constant(s).


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