Question

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

Answer 1

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.