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Show that the Signum Function f: R → R, given by
is neither one-one nor onto.
Asked by Lokayya Last Modified
Answer 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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Mayank Dadarwal
In a one-to-one function, given any y there is only one x that can be paired with the given y.
And for onto function Range should be equal to Co domain.
Now think little bit and try to solve without any help soo that you will remember.
Hint: Try to find pair such that it's not one one.
For onto write down range and co domain and check it's equal or not
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