Let `f : ZxxZ rarr Z` be defined by `f(n,m)=n+m` for all `(n,m) in ZxxZ` show that f is onto but not one-one.

If f : R rarr R be defined by f(x)=|x| , show that fof=f

Show that the function f : N rarr N defined by f(n){((n+1)/2 if n is odd),(n/2 if n is even):} is onto but not one-one.

Let f : W rarr W be defined as f(n)={(n-1, n is odd),(n+1, nis even):} Show that f is invertible such that f^-1=f

Let f : R rarr R be defined as f(x)=2x+3 . Show that f is invertible and find f^-1 : R rarr R .

Show that the function f : R rarr R defined by f(x)=[x] , where [x] is the greatest integer less than equal to x is neither one-one nor onto.

Let f:R rarr R is defined by f(x)=3x-2 and g:R rarr R is defined by g(x)=(x+2)/3 . Show that f.g=g.f .

If f : R rarr R be defined by f(x)=2x-3 and g : R rarr R be defined by g(x)= (x+3)/2 , show that fog=gof=I_R