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

is neither one-one nor onto.

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Solution

f: R → R is 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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Show that the Signum Function f: R → R, given by is neither one-one nor onto.

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

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