f: Z → Z given by f(x) = x3 - Vidyadip

Question

f: Z → Z given by f(x) = x³

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Answer

f: Z → Z is given by,

f(x) = x³

It is seen that for $\text{x},\text{y}\in\text{Z},$ f(x) = f(y) ⇒ x³ = y³ ⇒ x = y.

$\therefore$ f is injective.

Now, $2\in\text{N}.$ But, there does not exist any element x in domain Z such that f(x) = x³ = 2.

$\therefore$ f is not surjective.

Hence, function f injective but not surjective.

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