Let f : ( − 1 , 1 ) → B , be a function defined by f ( x ) = tan − 1 1 − x 2 2 x , then f is both one-one and onto when B is the interval

Question

Let f : ( − 1 , 1 ) → B , be a function defined by f ( x ) = tan − 1 1 − x 2 2 x ​ , then f is both one-one and onto when B is the interval

TestHub · Accepted Answer

Given f ( x ) = tan − 1 ( 1 − x 2 2 x ​ ) for x ∈ ( − 1 , 1 ) clearly range of f ( x ) = ( − 2 π ​ , 2 π ​ ) . ∴ co-domain of function = B = ( − 2 π ​ , 2 π ​ ) .

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