525b18f       1                     525b18f                      525b18f           f                     525b18f                 Questa non è una funzione perché da b

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f       a                     525b18f               partono due frecce verso l'insieme Y.

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f   Qual è, infatti, il valore di f(b)? 1 o 2?

                     525b18f 2                     525b18f                      525b18f                      525b18f                      525b18f                b

                     525b18f               3

 c

FUNZIONE INIETTIVA Û " x₁ ,x₂ Î X : x₁ ¹ x₂ Þ f(x₁) ¹ f(x₂) Û " y Î Y esista al più un x Î X tale che y = f(x)

A                     525b18f               f                     525b18f           B

                     525b18f           1                     525b18f                      525b18f                      525b18f                      525b18f    a

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f      d                     525b18f                  a                     525b18f                      525b18f       1

                     525b18f                      525b18f   2                     525b18f                      525b18f                      525b18f   b                     525b18f                      525b18f                      525b18f         b                     525b18f               2

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f      c                     525b18f                      525b18f     3 

                     525b18f         3                     525b18f                      525b18f                      525b18f                      525b18f              c                     525b18f                      525b18f                      525b18f                      525b18f         4

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f    Non è iniettiva perché

                     525b18f                      525b18f   Funzione iniettiva                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f     f(b) = f(c)

FUNZIONE SURRIETTIVA   Û " y Î Y, $ x Î X tale che y = f(x) Û f(X) = Y

                     525b18f    A                     525b18f                 B

                     525b18f                      525b18f                      525b18f        f

                     525b18f            1                     525b18f          

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f       a                     525b18f                      525b18f     1                     525b18f                      525b18f                   a

                     525b18f                      525b18f        2

                     525b18f      3                     525b18f                      525b18f                    b                     525b18f                      525b18f                      525b18f   2                     525b18f                      525b18f                    b

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f 3                     525b18f                      525b18f           c

                     525b18f               4                     525b18f                      525b18f                      525b18f           c                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f     d

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f     Non e surriettiva perché :

                     525b18f          Funzione surriettiva                     525b18f                      525b18f                      525b18f                      525b18f f(?) = 4

FUNZIONE BIETTIVA  Û " y Î Y, $ x Î X tale che y = f(x)  Se una funzione e biettiva, è anche iniettiva e surriettiva.

                     525b18f          x                     525b18f   f                     525b18f      y

                     525b18f                      525b18f                      525b18f                 1                     525b18f                      525b18f                      525b18f                      525b18f                 b

                     525b18f                      525b18f                      525b18f 2                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f      e

                     525b18f                      525b18f                      525b18f         3                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f          a

                     525b18f                      525b18f                      525b18f                 4

                     525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                      525b18f                    c

                     525b18f                      525b18f                      525b18f