Explain Equal and Identity functions?

1.	Explain Equal and Identity functions?
Answer» Two functions f and g are said to be equal if and only if (i) domain of f = domain of g (ii) co-domain of f = co-domain of g (iii) f (x) = g(x) for every x belonging to their common domain. Ex. Let A = {1, 2} and B = {3, 6}. Then f : A → B given by f (x) = x² + 2 and g : A → B given by g(x) = 3x are equal as: • f (1) = 3 = g(1), f (2) = 6 = g(2) • Both f and g have the same domain and co-domain. Identity Function: The identity function maps each member of the domain onto itself, i.e., if I is the identity function I: R → R then for all x ∈ R, I(x) = x.

Answer»

Two functions f and g are said to be equal if and only if

(i) domain of f = domain of g

(ii) co-domain of f = co-domain of g

(iii) f (x) = g(x) for every x belonging to their common domain.

Ex. Let A = {1, 2} and B = {3, 6}.

Then f : A → B given by f (x) = x² + 2 and g : A → B given by g(x) = 3x are equal as:

• f (1) = 3 = g(1), f (2) = 6 = g(2)

• Both f and g have the same domain and co-domain.

Identity Function:

The identity function maps each member of the domain onto itself, i.e., if I is the identity function I: R → R then for all x ∈ R,

I(x) = x.

Discussion