Check the injectivity and surjectivity of the following functions:
(i) f:Z→Z given by f(x)=x2
f:R→R is given by f(x)=x2. It is seen that f(-1)=f(1)=1 but −1≠1,
Therefore, f is not injective.
Now, −2∈R. But there does not exist any element x∈Z such that f(x)=x2=−2
Therefore, f is not surjective.
Hence, function f is neither injective nor surjective.