Relations and F...

A function f : X → Y  is said to be one – one and onto if

Let f : A → B and  g : B → C be two functions. Then the composition of f and g, denoted by gof, is defined as

A function f : X → Y is defined to be invertible, if

Let f : {2, 3, 4, 5} → {3, 4, 5, 9} and g : {3, 4, 5, 9} → {7, 11, 15} be functions defined as f (2) = 3, f(3) = 4, f (4) = f (5) = 5 and g (3) = g (4) = 7 and g (5) = g (9) = 11. Then gof is

if f : R → R and  g : R → R are given by f (x) = cos x and g(x) = 3x². Then

Let f : X → Y and g : Y → Z be two invertible functions. Then gof is