Q. 2 B 3.7( 19 Votes )

Check the injectivity and surjectivity of the following functions:

f : Z Z given by f (x) = x2

Answer :

It is given that f : Z Z given by f (x) = x2

We can see that f(-1) = f(1) = 1, but -1 ≠ 1

f is not injective.

Now, let -2 ϵ Z. But, we can see that there does not exists any x in Z such that

f(x) = x2 = -2

f is not surjective.

Therefore, function f is neither injective nor surjective.

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