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.
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.
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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