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

(iv) f: N \rightarrow N given by f(x) = x^3

Answers (1)

f : N\rightarrow N

f(x) = x^3

One- one:

x,y \in N  then f(x)=f(y)

                                  x^{3}=y^{3}

                                   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^{3}=3

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

Hence, f is injective but not surjective.

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