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