# NCERT Class 11-Math's: Chapter –2 Relations and Functions Part 2

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**Algebra of real functions**

(i) Addition of two real functions

Let and be any two real functions, where .

Then we define .

(ii) Subtraction of a real function from another

Let and be any two real functions, where .

Then, we define .

(iii) Multiplication by a Scalar

Let be a real function and α be any scalar belonging to R. Then the product αf is function from X to R defined by .

(iv) Multiplication of two real functions

Let and be any two real functions, where. Then product of these two functions i.e. is defined by

(v) Quotient of two real function

Let f and g be two real functions defined from X → R. The quotient of by denoted by is a function defined from as

**Note:**

Domain of sum function , difference function and product function .

where

Domain of quotient function

## Solved Examples

### Short Answer Type

**Question 1:**

Let and . Determine

(i)

(ii)

(iii)

(iv)

**Answer:**

Since and . Therefore,

(i)

(ii)

(iii) No, . Since A × B and B × A do not have exactly the same ordered pairs.

(iv)

Hence

**Question 2:**

Find *x* and *y* if:

(i)

(ii)

**Answer:**

(i)

Since , so

or

and

(ii)

or

**Example 3:**

If and , , find the set of ordered pairs such that ‘*a*’ is factor of ‘*b*’ and .

**Answer:**

Since

we have to find *a* set of ordered pairs (*a*, *b*) such that *a* is factor of *b* and .

Since is a factor of 4 and .

So is one such ordered pair.

Similarly, are other such ordered pairs. Thus the required set of ordered pairs is