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If the function f: RvecA given by f(x)=(...

If the function `f: RvecA` given by `f(x)=(x^2)/(x^2+1)` is surjection, then find `Adot`

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`f:R to A,f(x)=(x^(2))/(x^(2)+1)`
Here domain is all real numbers.
Since `f(x)` is onto, range must be same as codomain (A).
To find the range of the function,
`f(x)=1-(1)/(x^(2)+1)`
Now` x^(2)+1 ge 1 AA in R.`
`implies 0 lt (1)/(x^(2)+1) le 1`
`implies -1 le -(1)/(x^(2)+1) lt 0`
`implies 0 le 1 -(1)/(x^(2)+1) lt 1`
Thus, range is `[0,1).`
Hence codomain `A=[0,1).`
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