The function f: R → a where 'a' is a constant, is called a constant function. It is denoted by f(x) = a. The graph of a constant function is as shown in the figure given below; clearly a constant function is all-to-one.

  The function f(x): R → R defined such that f(x) = x ∀ x ε R is an Identify function. The graph of an identity function is shown in the figure given below.

Since an identity function is on-one and onto, so it is invertible.

Note: The inverse of an identity function is the identity function itself.

Examples

Check whether the following functions are identical with their inverse.

(a)    xy = 1

(b)    x² + y² = 1

Ans.  (a)    Yes          

        (b)    only for 0 < x < 1, 0 < y < 1