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 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 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.

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

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.

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

Examine continuity of the function f defined by. f(x)=x-5