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.

Let f: A to B and g: B to 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 the function f:A to B is one-one onto and g:B to A , is the inverse of f, then fog =?

Show that the function f(x)=3x+ 2 is one-one and onto

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.

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

Let A = R - {2}, B = R - {1}. If f : ArarrB is a function defined by f(x) = (x-1)/(x-2) , show that f is one-one and onto.

Consider functions f and g such that composite gof is defined and is one-one.Are f and g both necessarily one-one.

If f: R to R and g : R to R be two functions defined as respectively f(x)=2x and g(x)=x^(2)+2 , then prove that (i) f is one-one onto (ii) g is many-one into.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.