# NCERT Class 11-Math՚s: Chapter – 2 Relations and Functions Part 6 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 12**:

Let *f* and *g* be real functions defined by and .

(a) For what real numbers ?

(b) For what real numbers ?

**Answer**:

(a)

(b)

**Question 13**:

If *f* and *g* are two real valued functions defined as , then find.

(i)

(ii)

(iii)

(iv)

**Answer**:

(i)

(ii)

(iii)

(iv)

**Question 14**:

Express the following functions as set of ordered pairs and determine their range.

**Answer**:

(i)

**Question 15**:

Find the values of *x* for which the functions

are equal

**Answer**:

## Long Answer Type

**Question 16**:

Is a function? Justify. If this is described by the relation, , then what values should be assigned to and ?

**Answer**:

Yes,

**Question 17**:

Find the domain of each of the following functions given by

(i)

(ii)

(iii)

(iv)

(v)

**Answer**:

(i)

(ii)

(iii)

(iv)

(v)

**Question 18**:

Find the range of the following functions given by

(i)

(ii)

(iii)

(iv)

(**Hint**:

**Answer**:

(i)

(ii)

(iii)

(iv)

**Question 19**:

Redefine the function

**Answer**: