Answer:

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Step-by-step explanation:

A function f: A → B is SAID to be an Identity function if f(x) = x for all x ∈ A that means it always returns the same value that is used as its input.

Identity function is DENOTED by I (FIRST letter of Identity).

Identity function

Constant function:

A function f: A → B is said to be a constant function if there is an ELEMENT m ∈ B such that f(x) = m for all elements belongs to A.

That means the range of the function contains only one element.

Example:

Let f : A → B is a function defined as f(x) = m as x ∈ A, that is, f(p) = m, f(q) = m, f(r) = m, f(s) = m, f(t) = m.

So, 'f' is a constant function defined from A → B as f(x) = m for all x ∈ A.

Identity function

Even function:

A function y = f(x) is said to be an even function, if f(– x) = f (x) ∀ x ∈ Domain (f).

For example: y = | x | is an even function since f(– x) = f (x) ∀ x ∈ Domain (f).

The graph of an even function is symmetric about y axis.

Odd function:

A function y = f(x) is said to be an odd function if f(– x) = – f (x), ∀ x  Domain (f).

The graph of an odd function is symmetrical about the origin and passes through origin.

Equal functions:

Two functions f and g defined on the same domain D are said to be equal, if f(x) = g(x) for all x ∈ D.

For example: let f and g are two functions defined as f(x) = x + 2 for x ∈ N and g(x) = x + 2 for x ∈ N, then f and g are called equal functions.

Real function:

If f : A → B such that A ⊑ R, then f is said to be a real variable function.

If f : A → B such that B ⊑ R, then f is said to be a real valued function.

If f : A → B and A, B are both subsets of the set of real numbers (R), then f is called a real function.

If f (x) is a real function, then  is always an even function and  is always an odd function. But f(x) = 0 is both even and odd.