Show that the function `f : R rarr R`, defined by `{(-1,x<0),(0,x=0),(1,x>0):}` is neither one-one nor onto.

Show that the function f : R rarr R , defined by f(x)=|x| is neither one-one nor onto.

Show that the function f: R to R defined by f(x)=2x^(2) , is neither one - one onto.

Show that the function f : R rarr R defined by f(x)=x^2+4 is not invertible.

Show that the function f : R_0 rarr R_0 defined by f(x)=1/x , where R_0 is the set of nonzero real numbers is bijective.

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.

Prove that the function f:N rarr N defined by f(x)=x^2+2 is one-one but not onto.

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.

Find the value of k for which the function f : R rarr R defined by f(x)=5+kx,kne0 is the inverse of itself.

Show that the function f : N' rarr Z, f(x)=100-x^2 is not bijective.