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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

 

Answers (1)
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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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