Show that the function f: N → Z, defined by
is both one - one and onto.
f(1) = 0
f(2) = - 1
f(3) = 1
f(4) = - 2
f(5) = 2
f(6) = - 3
Since at no different values of x we get same value of y ∴f(n) is one –one
And range of f(n) = Z = Z(codomain)
∴ the function f: N → Z, defined by
is both one - one and onto.