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Relations and Functions
Question
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Show that the function f : R →R , defined as f (x) = x2 , is neither one-to-one nor onto.

Answer

Here f(x) = x2 Df = R Now 1,–1 ∈ R Also f (1)= 1, f (–1) = 1 Now 1 ≠ –1 but f (1) = f (–1)
∴ f is not one-to-one.
Again, the element – 2 in the co-domain of R is not image of any element x in the domain R.
∴ f is not onto.

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