Q. 5 P5.0( 2 Votes )

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, given by f(x) = 1 + x2


Check for Injectivity:


Let x,y be elements belongs to R i.e such that


So, from definition


f(x) = f(y)


x2 + 1 = y2 + 1


x2 = y2


±x = ±y


Therefore, either x = y or x = – y or x ≠ y


Hence f is not One – One function


Check for Surjectivity:


1 be element belongs to R i.e be arbitrary, then


f(x) = 1


x2 + x = 1


x2 + x – 1 = 0



Above value of x not belongs to R for y < 1


Therefore f is not onto


Thus, It is also not Bijective function


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