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

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 rarr R defined by f(x)=x^2+4 is not invertible.

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

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 : R rarr R , defined by {(-1,x 0):} is neither one-one nor onto.

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.

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 to R defined by f(x)=2x^(2) , is neither one - one onto.