`f : N -> A` where `A= {0,1}` defined by `f(x) = 0 if x is odd, 1 if x is even`. Then `f` is

Show that f : N rarr N given by : f(x) = {x+ 1, if x is odd x - 1 , if x is even is both one-one and onto.

Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x - 1), if x is even) :} is both one-one and onto.

Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1 , "if x is even"):} is both one - one and onto .

Show that f : N to N , given by f(x)= {(x+1", if x is odd"),(x-1", if x is even"):} is bijective (both one-one and onto).

Let f: N uu {0} rarr N uu {0} be defined by : f(n)= {(n+1, if n is even),(n-1, if n is odd):} .Show that f is invertible and f =f^-1 .

Show that f:N rarr N given by f(x)={{:(x+1", if x is odd"),(x-1", if x is even"):} is both one-one and onto.

If function f:ZtoZ is defined by f(x)={{:((x)/(2), "if x is even"),(0," if x is odd"):} , then f is

Examine the continuity of f, where f is defined by f(x) = {:{(sin x - cosx , if x ne 0),(-1, if x = 0):} .