Constant Function and the Identity Function

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.

                                              graph-of-a-constant-function 

  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.

                                          graph-of-an-identity-function

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

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