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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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To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

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