Let f and g be two functions such that `gof = I_A` and `fog = I_B`. Then; f and g are bijections and `g = f^-1`

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)

Let A be a non-empty set and f : A rarr A, g : A rarr A be two functions such that fog = I_A = gof , show that f and g are ijections and that g = f^-1

Let f: A to B; g: B to A be two functions such that gof = I_A . Then; f is an injection and g is a surjection.

Let f: A to B; g: B to A be two functions such that fog = I_B . Then; f is a surjection and g is an injection.

Let f:A rarr B;g:B rarr A be two functions such that gof=I_(A). Then; f is an injection and g is a surjection.

Let f:A rarr B;g:B rarr A be two functions such that fog=I_(B). Then; f is a surjection and g is an injection.

Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id_(X) and fog = id_(y) , then show that f is bijective and (ii) g =f^(-1)

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: