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If the function f: R -{1,-1} to A defind...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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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