# 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

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