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Q.2 Check the injectivity and surjectivity of the following functions:

(ii) $f : Z \rightarrow Z$ given by $f(x) = x^2$

Answers (1)

S seema garhwal

$f : Z \rightarrow Z$

$f(x) = x^2$

One- one:

For $-1,1 \in Z$ then $f(x) = x^2$

$f(-1)= (-1)^{2}$

$f(-1)= 1$ but $-1 \neq 1$

$\therefore$ f is not one- one i.e. not injective.

For $-3 \in Z$ there is no x in Z such that $f(x)=x^{2}= -3$

$\therefore$ f is not onto i.e. not surjective.

Hence, f is neither injective nor surjective.

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