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Classify the foll

Answer :

TIP: One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.


So, is One – One function


a≠b


f(a)≠f(b) for all


f(a) = f(b)


a = b for all


Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.


So, is Surjection iff for each , there exists such that f(a) = b


Bijection Function: – A function is said to be a bijection function if it is one – one as well as onto function.


Now, f : R R, defined by f(x) = sin2x + cos2x


Check for Injectivity and Check for Surjectivity


Let x be element belongs to R i.e such that


So, from definition


f(x) = sin2x + cos2x


f(x) = sin2x + cos2x


f(x) = 1


f(x) = constant


We know that a constant function is neither One – One function nor onto function.


Thus, It is not Bijective function


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