Q. 34.6( 5 Votes )

Show that the function f : R R : f (x) = x2 is neither one-one nor onto.

Answer :

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


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