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Show that the function f : R ->R, define...

Show that the function `f : R ->R`, defined as `f(x)=x^2`, is neither one-one nor onto.

Text Solution

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We have `f(-1) =(-1)^(2)=1 " and " f(1) =1^(2) =1`
Thus two diffierent elements in R have the same image
`:.` f is not one-one
If we consider -1 in the codomain R then it is clear that there is no elements in R whose image is -1
`:. ` f is not onto.
Hence f is neither one-one nor onto.
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