InterviewSolution
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InterviewSolution
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If the function `f: R -{1,-1} to A` definded by `f(x)=(x^(2))/(1-x^(2))`, is surjective, then A is equal to(A) `R-{-1}`(B) `[0,oo)`(C) `R-[-1,0)`(D) `R-(-1,0)`A. `R-{-1}`B. `[0,oo)`C. `R-[-1,0)`D. `R-(-1,0)` |
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Answer» Correct Answer - C Given, function `f: R -{1,-1} to A` defined as `f(x)=(x^(2))/(1-x^(2))=y" " `(let) `rArr x^(2)=y(1-x^(2)) " " [ because x^(2) ne 1]` `rArr x^(2)(1+y)=y` `implies x^(2)=(y)/(1+y) " "["provided "y ne -1]` ` because x^(2) ge 0` `rArr (y)/(1+y) ge 0 rArr y in (-oo,-1)cup [0,oo)` Since for surjective function, range of f = codomain `therefore` Set A should be `R-[-1,0).` |
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