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`

Statement -I: f: A to B is one -one and g: B to C is a one-one function, then gof : A to C is one-one Statement-II: If f: A to B, g : B to A are two functions such that gof =I_(A) and fog=I_(B) , then f=g^(-1) . Statement-III: f(x) =sec^(2)x- tan^(2)x, g(x) ="cosec"^(2)x-cot^(2)x , then f=g. Which of the above statements is/are true:

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

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

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

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

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

Let f and g be two functions such that gof=L_(A) and fog=L_(B). Then; f and g are bijections and g=f^(-1)

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