Type of Functions

Type of Functions

(a) One-One (Injective)

If x1, x2 ∈ A

then f(x₁) = f(x₂) ⇒ x₁ = x₂

and x1 ≠ x₂ ⇒ f(x₁) ≠ f(x₂)

(b) Many-One

If x1, x2 ∈ A, f(x1) = f(x2) ⇒ x1 ≠ x2

(c) Onto (Surjective) and Into

If f(A) = B i.e. Range = co-domain then the function is ONTO (Surjective) and If f(A) ⊂ B i.e. Range ⊂ co domain then the function is INTO.

One-One onto functions are also called bijective functions.