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 : NrarrN , 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 defined by : f(n)= {((n+1)/2, if n is odd),(n/2, if n is even):} is many-one onto function.

The function f: N rarr N , given by f(x) = 2x is

Show that the signum function f : R to R given by: f(x) = {{:(1, if x gt 0),(0, if x =0),(-1, if x lt 0):} is neither one-one nor onto.

Let f: N rarr N be defined by : f(n)= {(n+1, if n is odd),(n-1, if n is even):} .Show that f is a bijective function.

Show that the function f: N rarrN given by f(1) = f(2) = 1 and f(x) = x-1 AAxgt2 is onto but not one-one.

Show that the function f:N rarr N given by f(x) = 4x is one-one, but not onto.

Show that the function f:N rarr N given by f(x) = 5x is one-one but not onto.

Show that function f: Nrarr N given by f(x) = x^2 is neither one-one nor onto.

Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x) =x-1 , for every x > 2 is onto but not one-one.