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**Exercise 2.3**

**1. Which of the following are functions? Give reasons. If it is a function determine its domain and range.**

**(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}**

**(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}**

**(iii) {(1, 3), (1, 5), (2, 5)}**

**Ans. (i)** Given: Relation is {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

All values of are distinct. Each value of has a unique value of

Therefore, the relation is a function.

Domain of function = {2, 5, 8, 11, 14, 17}

Range of function = {1}

**(ii)** Given: Relation is {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

All values of are distinct. Each value of has a unique value of

Therefore, the relation is a function.

Domain of function = {2, 4, 6, 8, 10, 12, 14}

Range of function = {1, 2, 3, 4, 5, 6, 7}

**(iii)** Given: Relation is {(1, 3), (1, 5), (2, 5)}

This relation is not a function because there is an element 1 which is associated to two elements 3 and 5.

**2. Find the domain and range of the following real functions:**

**(i) **

**(ii) **

**Ans. (i)** Given: . The function is defined for all real values of

Domain of the function = R

Now, when then

When

When

Therefore, for all real values of

Range of function =

**(ii)** Given: .

The function is not defined when

Domain of function =

= =

Range of function =

**3. A function **** is defined by **** Write down the values of:**

**(i) **

**(ii) **

**(iii) **

**Ans. **Given:

**(i) **Putting

**(ii) **Putting

**(iii) **Putting

**4. The function **** which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by **** Find:**

**(i) **

**(ii) **

**(iii) **

**(iv) The value of C when **

**Ans. **Given:

**(i) **Putting C = 0,

**(ii) **Putting C = 28,

**(iii) ** Putting C = –10,

**(iv) **Putting = 212,

**5. Find the range of each of the following functions:**

**(i) **

**(ii) **** is a real number.**

**(iii) **** is a real number.**

**Ans. (i)** Given: , R and

Range of function

= =

**(ii)** Given: R

for R

Range of function

= =

**(iii)** Given: , R

Range of function = R

I cant understand 2nd question 2nd part

you haven’t even explained the questions in which you take out the range

2nd question kuch vi smj ni aaya..