question_answer 63)

Give examples of two functions f : N  N and       g : N  N such that gof is onto but f is not onto.  

Answer:

Let f(x) = x + 1 and g(x) =       Let  be any element                x + 1        f(x)             Hence f is not onto.       Also gof : N  N is such that       (gof) (x) = g(f(x)) =g(x +1)          = (x + 1) ? 1 =x             Hence gof is onto.