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 rarr B and are onto,then are onto,then is also onto.

If f:A rarr B and g:B rarr C are onto functions show that gof is an onto function.

If functions f:A to B and g : B to A satisfy gof= I_(A), then show that f is one-one and g is onto.

Statement I: f : A->B is one - one and g : B->C is a one - one function, then gof :A->C is one - one Statement II : If f:A->B, g:B->A are two functions such that gof=IA and fog=IB, then f=g-1. Statement III : f(x)=sec 2x-tan2x,g(x)=cosec2x-cot2x, then f=g

If f:A rarr B and g:B rarr C are one-one functions,show that gof is one-one function.

Let f:A rarr B and g:B rarr C be two functions.Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

If f: A-> B and g: B-> C be the bijective function, then (gof)^(-1) is:

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

Consider function f : A to B and g : B to C (A, B, sube R) such that (gof) ""^(-1) exists then