# NCERT Class 11-Math's: Chapter –2 Relations and Functions Part 3

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**Question 4:**

Find the domain and range of the relation R given by

**Answer:**

When . Again for,

. Again for

Thus where Domain

Range of

**Question 5:**

Is the following relation a function? Justify your answer

(i)

(ii)

**Answer:**

Since

So does not have a unique image. Thus is not a function.

(iii)

For every there will be unique image as .

Therefore is a function.

**Question 6:**

Find the domain for which the functions

are equal.

**Answer:**

For

Thus domain for which the function

**Question 7:**

Find the domain of each of the following functions.

(i)

(ii)

**Answer:**

(i) is a rational function of the form where

Now and hence domain of the given function is .

(ii)

where and

The domain of

and the domain of. Therefore

Domain of

**Question 8:**

Find the range of the following functions given by

(i)

(ii)

**Answer:**

Thus the range of

(ii) The domain of , where given by

For the range, let

Then

Or

Since

Thus range of

**Question 9:**

Redefine the function which is given by

**Answer:**