NCERT Solutions class-11 Maths Exercise 2.3

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.

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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 =

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

(i)

(ii)

(iii)

Ans. Given:

(i) Putting

(ii) Putting

(iii) Putting

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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,

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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