Find the domain and range of the real function defined by `f(x) =(1)/( – InterviewSolution

1.	Find the domain and range of the real function defined by `f(x) =(1)/((1-x^(2)).`
Answer» Clearly `(1)/((1-x^(2))` is not defined when `1-x^(2) =0` i.e., when `x= +- 1` `:.` dom `(f) =R - {-1 ,1}` Also `y=(1)/((1-x^(2)) rArr (1-x^(2) =(1)/(y) rArr sqrt(1-(1)/(y))` clearly x is not defined when `(1-(1)/(y)) lt 0 " or " 1 lt (1)/(y) " or " y lt 1` `:.` range `(f ) =R- { y in R : y lt 1}={ y in R : y ge 1}`

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