# NCERT Solutions class-11 Maths Exercise 2.3 ## myCBSEguide App

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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 ### 3 thoughts on “NCERT Solutions class-11 Maths Exercise 2.3”

1. I cant understand 2nd question 2nd part

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

3. 2nd question kuch vi smj ni aaya..