Q

# Check the injectivity and surjectivity of the following functions f defined from Z to Z given by f(x) = x to the power 2

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

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

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$f : Z \rightarrow Z$

$f(x) = x^2$

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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