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

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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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