Definition 9 A function f : X → Y is defined to be invertible, if there exists a function
g : Y → X such that  gof = IX and fog = IY The function g is called the inverse of f  and
is denoted by f –1 Thus, if f is invertible, then f must be one-one and onto and conversely, if f is
one-one and onto, then f must be invertible This fact significantly helps for proving a
function f to be invertible by showing that f is one-one and onto, specially when the
actual inverse of f is not to be determined