Types of Functions,One-One Function or Injective Function,Onto or Surjective Function,Bijective Function or One-One Onto function,Invertible Function

Types of Functions

One-One Function or Injective Function: A function f : X → Y is defined to be one-one (or injective), if the images of distinct elements of X under f are distinct, i.e., for every x₁, x₂ in  X, implies  that f (x₁) = f (x₂). Otherwise, f is called many-one.

Onto or Surjective Function: A function f : X → Y is said to be onto (or surjective), if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f (x) = y.

Bijective Function or One-One Onto function: A function f : X → Y is said to be one-one and onto (or bijective), if f is both one-one and onto.

Invertible Function: A function f : X→  Y is defined to be invertible, if there exists a function g : Y → X such that  gof = I_X  and fog = I_Y. The function g is called the inverse of f  and is denoted by f^-1.