Question

function of f:R-R defined by​

Answer 1

For x1, x2 ∈ R, consider We note that there are point, x1 and x2 with x1 ≠ x2 and f (x1) = f (x2), for instance, if we take x1 = 2 and x2 = 1/2, then we have f (x1) =2/5 and f(x2) =2/5 but 2 ≠ 1/2 . Hence f is not one-one. Also, f is not onto for if so then for 1∈R ∃ x ∈ R such that f (x) = 1 which gives  x/(x2+1) =1. But there is no such x in the domain R, since the equation x2 – x + 1 = 0 does not give any real value of x ..

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Answer 2

For x1, x2 ∈ R, consider We note that there are point, x1 and x2 with x1 ≠ x2 and f (x1) = f (x2), for instance, if we take x1 = 2 and x2 = 1/2, then we have f (x1) =2/5 and f(x2) =2/5 but 2 ≠ 1/2 . Hence f is not one-one. Also, f is not onto for if so then for 1∈R ∃ x ∈ R such that f (x) = 1 which gives x/(x2+1) =1. But there is no such x in the domain R, since the equation x2 – x + 1 = 0 does not give any real value of x.

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