Q. 185.0( 2 Votes )

Give examples of two surjective function f1 and f2 from Z to Z such that f1 + f2 is not surjective.

Answer :

TIP:


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


Let, f1: Z Z and f2: Z Z be two functions given by (Examples)


f1(x) = x


f1(x) = – x


From above function it is clear that both are Onto or Surjective functions


Now,


f1 + f2 : Z Z


(f1 + f2)(x) = f1(x) + f2(x)


(f1 + f2)(x) = x – x


(f1 + f2)(x) = 0


Therefore,


f1 + f2 : Z Z is a function given by


(f1 + f2)(x) = 0


Since f1 + f2 is a constant function,


Hence it is not an Onto/Surjective function.


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