{"id":4576,"date":"2016-05-17T09:49:00","date_gmt":"2016-05-17T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-3\/"},"modified":"2016-05-17T10:17:56","modified_gmt":"2016-05-17T04:47:56","slug":"ncert-solutions-class-11-maths-exercise-2-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-3\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 2.3"},"content":{"rendered":"

Exercise 2.3<\/strong><\/p>\n

1. Which of the following are functions? Give reasons. If it is a function determine its domain and range.<\/strong><\/p>\n

(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}<\/strong><\/p>\n

(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}<\/strong><\/p>\n

(iii) {(1, 3), (1, 5), (2, 5)}<\/strong><\/p>\n

Ans. (i)<\/strong> Given: Relation is {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}<\/p>\n

All values of are distinct. Each value of has a unique value of <\/p>\n

Therefore, the relation is a function.<\/p>\n

Domain of function = {2, 5, 8, 11, 14, 17}<\/p>\n

Range of function = {1}<\/p>\n

(ii)<\/strong> Given: Relation is {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}<\/p>\n

All values of are distinct. Each value of has a unique value of <\/p>\n

Therefore, the relation is a function.<\/p>\n

Domain of function = {2, 4, 6, 8, 10, 12, 14}<\/p>\n

Range of function = {1, 2, 3, 4, 5, 6, 7}<\/p>\n

(iii)<\/strong> Given: Relation is {(1, 3), (1, 5), (2, 5)}<\/p>\n

This relation is not a function because there is an element 1 which is associated to two elements 3 and 5.<\/p>\n

\n

2. Find the domain and range of the following real functions:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong><\/p>\n

Ans. (i)<\/strong> Given: . The function is defined for all real values of <\/p>\n

Domain of the function = R<\/p>\n

Now, when then <\/p>\n

<\/p>\n

When <\/p>\n

<\/p>\n

When <\/p>\n

<\/p>\n

Therefore, for all real values of <\/p>\n

Range of function = <\/p>\n

(ii)<\/strong> Given: .<\/p>\n

The function is not defined when <\/p>\n

Domain of function = <\/p>\n

= = <\/p>\n

Range of function = <\/p>\n

\n

3. A function <\/strong> is defined by <\/strong> Write down the values of:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong><\/p>\n

(iii) <\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

(i) <\/strong>Putting <\/p>\n

<\/p>\n

(ii) <\/strong>Putting <\/p>\n

<\/p>\n

(iii) <\/strong>Putting <\/p>\n

<\/p>\n

\n

4. The function <\/strong> which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by <\/strong> Find:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong><\/p>\n

(iii) <\/strong><\/p>\n

(iv) The value of C when <\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

(i) <\/strong>Putting C = 0,<\/p>\n

(ii) <\/strong>Putting C = 28,<\/p>\n

(iii) <\/strong> Putting C = \u201310, <\/p>\n

(iv) <\/strong>Putting = 212, <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

5. Find the range of each of the following functions:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) <\/strong> is a real number.<\/strong><\/p>\n

(iii) <\/strong> is a real number.<\/strong><\/p>\n

Ans. (i)<\/strong> Given: , R and <\/p>\n

<\/p>\n

<\/p>\n

Range of function<\/p>\n

= = <\/p>\n

(ii)<\/strong> Given: R<\/p>\n

for R<\/p>\n

<\/p>\n

Range of function<\/p>\n

= = <\/p>\n

(iii)<\/strong> Given: , R<\/p>\n

Range of function = R<\/p>\n","protected":false},"excerpt":{"rendered":"

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, … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4576","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 2.3 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 2.3 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"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, ... 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