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

Prove that the function f : R rarr R, f(x)=5x^3-8 is bijective.

Let A=R-{3} and B=R-{1} be two given sets. Prove that the function f : A rarr B, f(x)= (x-2)/(x-3) is bijective.

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

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

Prove that the function f : N-{1} rarr N, f(n)= the highest prime factor of n is neither one-one nor onto.