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: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.

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

Let f and g be two real functions;such that fog is defined.If g is continuous at x=a and f is continuous at g(a); show that fog is continuous at x=a

Let f and g be two real functions; continuous at x=a Then f+g and f-g is continuous at x=a

Let f : R rarr R and g : R rarr R be two functions such that fog (x) = sin x^(2) and gof (x) = sin^(2)x . Then , find f(x) and g(x).

If f and g are two decreasing function such that fog is defined,then fog will be-

Let f and g be two real functions; continuous at x=a Then fg and (f)/(g) ia continous at x=a; provided g(a)!=0

Let f:A to A and g:A to A be two functions such that fog(x)=gof (x)=x for all x in A Statement-1: {x in A: f(x)=g(x)}={x in A: f(x)=x}={x in A: g(x)=x} Statement-2: f:A to A is bijection.