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The function f: Rvec[-1/2,1/2] defined a...

The function `f: Rvec[-1/2,1/2]` defined as `f(x)=x/(1+x^2),` is : Surjective but not injective (2) Neither injective not surjective Invertible (4) Injective but not surjective

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Here, `f(x) = x/(1+x^2)`
`:. f'(x) = ((1+x^2) - x(2x))/(1+x^2)^2`
`=> f'(x) = (1-x^2)/(1+x^2)^2`
So, `f'(x)` is not always greater than `0` and not always less than `0.`
It means `f(x)` is not one - one or injective function.
Now, let `y` is the range of `f(x).`
Then,
`y = x/(1+x^2)`
...
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