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.