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Types of Functions

One to one ( injective function )​

An injective function is a function maps distinct elements of its domain two distinct element of its co-domain

  • if |A| lessthan equal |B|
  • Number of possible functions = npm = P(n, m)

On-to (Surjective function)​

A function F:A->B said to be on-to function if and only if every element of B is mapped by at least one element of A

  • F:A->B possible only if |B| less equal |A|
  • no of onto funcion possible, let |A| = m, |B| = n, then possible function is n^m - nc1 (n-1)^m + 2c2 (n-2)^m .....+ (-1)^n * ncn-1 * 1^m

Bijective funcion​

Bijective function is bot one to one and on-to function combined

  • |A| = |B|
  • possible funcions = n!

Inverse of function​

  • An inverse function (Anti function) is a function that reverse another function
  • If the function F applied to an input X gives a result of Y then applying its inverse function F` to Y gives the result of X and vice versa
  • f(x) = y then f`(y) = x

Function Composition​

function Composition is an operation that takes two functions F and G produces a function H such that H(x) = G(F(x))

  • F:x->y
  • G:y->z
  • G(F(x)) = z