Q

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

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

(i) $f : N\rightarrow N$ given by $f(x) = x^2$

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$f : N\rightarrow N$

$f(x) = x^2$

One- one:

$x,y \in N$  then $f(x)=f(y)$

$x^{2}=y^{2}$

$x=y$

$\therefore$  f is one- one i.e. injective.

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

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

Hence, f is injective but not surjective.

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