a) Let f: R→ R be given by f(x) = x2.Prove that the function is not injective
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We can suppose an example for this
As 9 = f(3) = f(-3) but 3 is not equal to -3, so it is not injective or one to one
As 9 = f(3) = f(-3) but 3 is not equal to -3, so it is not injective or one to one
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Injective function means that each element of domain is mapped on to a unique element of the codomain. That is, one-to-one mapping. It is not necessary that all elements of codomain be mapped.
f(x) = f(-x) = x^2 ∀ x in R. so two elements map onto the same element in the codomain.
So the inverse of the function does not exist. and it is not an injective function.
f(x) = f(-x) = x^2 ∀ x in R. so two elements map onto the same element in the codomain.
So the inverse of the function does not exist. and it is not an injective function.
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