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Question 5

Show that the Signum Function f : R → R, given by

is neither one-one nor onto.

Answer

f : R → R, given by 

It is seen that f(1) = f(2) = 1, but 1 ≠ 2.

f is not one-one.

Now, as f(x) takes only 3 values (1, 0, or - 1) for the element - 2 in co-domain R, there does not exist any x in domain R such that f(x) = - 2.

∴ f is not onto.

Hence, the signum function is neither one-one nor onto.

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