Show that the function f : R → R : f (x) = x2 is neither one-one nor onto.
To prove: function is neither one-one nor onto
Given: f : R → R : f (x) = x2
Solution: We have,
f(x) = x2
For, f(x1) = f(x2)
⇒ x12 = x22
⇒ x1 = x2 or, x1 = -x2
Since x1 doesn’t has unique image
∴ f(x) is not one-one
f(x) = x2
Let f(x) = y such that 
⇒ y = x2
If y = -1, as 
Then x will be undefined as we cannot place the negative value under the square root
Hence f(x) is not onto
Hence Proved
1