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

(v)  f : Z \rightarrow Z given by f(x) = x^3

 

Answers (1)

f : Z \rightarrow Z

f(x) = x^3

One- one:

For   (x,y) \in Z  then f(x) = f(y)

                                            x^{3}=y^{3}

                                            x=y 

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

For  3 \in Z  there is no x in Z 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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