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Check the injectivty and surjectiveity o...

Check the injectivty and surjectiveity of the following functions :
(i) ` f : N to N ` given by `f (x) = x ^(2)`
(ii) `f :Z to Z` given by `f (x) = x ^(2)`
(iii) `f : R to R` given by `f (x) =x ^(2)`
(iv) `f : N to N` given by `f (x) = x ^(3)`
(v) ` f : Z to Z` given by `f (x) = x ^(3)`

Text Solution

Verified by Experts

The correct Answer is:
(i) Injective but not surjective
(ii) Neither injective nor surjective
(iii) Neither injective nor surjective
(iv) Injective but not surjective
(v) Injective but not surjective
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