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Let f: R to R be defined by f(x)=(x)/(1...

Let `f: R to R ` be defined by `f(x)=(x)/(1+x^(2)), x in R.` Then, the range of f is

A

`R-[-1/2 , 1/2]`

B

`-[-1,1]`

C

`[-1/2,1/2]`

D

`(-1,1),-{0}`

Text Solution

Verified by Experts

The correct Answer is:
C
`f:R to R f(x)=x/(1+x^2) `
So, `y=x/(1+x^2) rArr yx^2-x+y=0`
Now, `D ge 0 rArr 1-4y^2 ge 0 rArr -1/2 le y le 1/2 `
Also , for x=0, y=0 . So , y=0 is part of range.
`therefore y in [-1/2,1/2]`
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