Question

Find the domain and range of the real function defined by
`f(x) =(1)/((1-x^(2)).`

Answer 1

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}`