If f and g are two bijections; then gof is a bijection and `(gof)^-1 = f^-1 o g^-1`

If f: A-A ,g: A-A are two bijections, then prove that fog is an injection (ii) fog is a surjection.

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

If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=x+2 , show that f and g are bijective maps. Verify that (gof)^(-1)=f^(-1)\ og^(-1) .

If f: A->A ,\ \ g: A->A are two bijections, then prove that fog is an surjection.

Let f:A to B and g:B to C be bijection, then (fog)^(-1) =

Letf: A rarr B be a function then show that f is a bijection if and only if there exists a function g:B rarr A such that fog =I_(B)&gof=I_(A)& in this case g=f^(-1)

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(x)=sqrt(1-x) and g(x)=log x are two functions,then describe functions fog and gof.

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.

A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not? In case it is a bijection, find f^(-1)(3) .