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.