Are f and g both necessarily onto, if gof is onto ?

Consider functions f and g such that composite gof is defined and is one one Are f and g both necessarily one-one.

Show that if f: A to B and g: B to C are onto, then gof : A to C is also onto.

Show that if f: A to B and g : B to C are onto, then gof A to C is also onto.

Show that if f : A to B and g: B to C are one-one, then gof: A to C is also one-one.

Show that if f: AtoB and g: Bto C are onto,then go f : AtoC is also onto.

Let A = {1, 2, 3, 4} and B = {1, 2} . Then the number of onto functions from A onto B is

Let f:(-1,1)toB be a function defined by : f(x)=tan^(-1)""(2x)/(1-x^2) , then f is both one-one and onto when B is the interval :

Show that the function f:N to N, given by f (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.

the number of one - one and onto mapping from A to B where n (A) = 6 and n (B ) = 7 is :