The numbers are written within a set of parentheses and separated by a comma. Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Mapping Diagram-2, 2, 4, 5, 6. Relation and Function Class 11 NCERT Solutions PDF. Relations and Functions Let’s start by saying that a relation is simply a set or collection of ordered pairs. A simple cipher takes a number and codes it, using the function f(x) = 3x−4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x (by drawing the lines). Problem : What is the domain of the relation in the following mapping diagram? JEE Main Relations and Functions Previous Year Questions With Solutions, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16. This is an example of an ordered pair. function is not injective as it changes sign in different intervals. The pair (7, 4) is not the same as (4, 7) because of the different ordering. This video looks at relations and functions. Find the inverse of this function and determine whether the inverse is also a function. Find functional values. Relations and Functions; Problems; Domain; Problems; Range; Problems; Terms; Writing Help. a relation which describes that there should be only one output for each input Solution : Empty Relations, Inverse Relations, Universal Relations, Identity Relations, Reflexive Relations, Symmetric Relations, Transitive Relations. f(x) is minimum when |sin x| = 0 and |cos x| = 1, f(x) is max when |sin x| = 1 and |cos x| = 0, Question 5: If f:R-> R satisfy f(x + y) = f(x) + f(y), for all x, y Є R and f(1) = 7 then ∑r=1nf(r)\sum_{r=1}^n f(r)∑r=1nf(r) is, Therefore, f(3) = f(1) + f(2) = 7 + 2(7) = 3(7), => ∑r=1nf(r)=7(1+2r+…+n)=7n(n+1)2\sum_{r=1}^n f(r) = 7(1 +2r+…+n) = \frac{7n(n+1)}{2}∑r=1nf(r)=7(1+2r+…+n)=27n(n+1), Question 6: The range of the function f(x) = 7-xPx-3 is, Question 7: If fx(x) = 1/k (sinkx + coskx) where x Є R and k ≥ 1, then f4(x) – f6(x) is, (a) 1/6 (b) 1/4 (c) 1/5 (d) 1/12, f4(x) = 1/4 (sin4x + cos4x) and f6(x) = 1/6 (sin6x + cos6x), Now, f4(x) – f6(x) = 1/4 (sin4x + cos4x) – 1/6 (sin6x + cos6x) …(1), Using identity: (a4 + b4) = (a2 + b2)2 – 2a2b2 and (a6 + b6) = (a2 + b2)3 – 3a2b2(a2 + b2) and also, we know, sin2 x + cos2x = 1, (1) => f4(x) – f6(x) = 1/4(1 – 2 sin2 x cos2x) – 1/6 (1 – 3 sin2 x cos2x), Question 8: The function f: N -> N defined by f(x) = x – 5[x/5], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is. This is the Aptitude Questions & Answers section on & Sets, Relations and Functions& with explanation for various interview, competitive examination and entrance test. An ordered-pair number is a pair of numbers that go together. Exchanging Singapore Dollar to Indian Rupee is. If n = odd: clearly shown that function is one-one and onto. f(x) is increasing in [0, 2] and decreasing in [2, 3]. So in a relation, you have a set of numbers that you can kind of view as the input into the relation. Nothing really special about it. Consider x in intervals of 5 natural numbers. The answer is (e). One to one function or Injective function, Many to one function, Onto Function or Surjective function, One-one and Onto function or Bijective function. From the above graph, we can conclude that f(x) is neither one-one nor onto. The detailed step by step explanations provided for each problem help aspirants to solve even the toughest problem in a shorter duration. An ordered pair, commonly known as a point, has two components which are the x and y coordinates. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. Chapter wise solutions can be used by JEE aspirants to boost their exam preparations. (f o g o g o f) (x) = [sin (sin x2)]2 …(i), But, sin x2 = π/2 can not be a solution as sin x Є [-1, 1], =>x2 = n π or x = ± √nπ where n Є {0, 1, 2, 3,…..}, Question 3: A function f from the set of natural numbers to integers defined by. The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. Chapter 2 Relations & Functions: Ordered pairs, Cartesian product of sets. Problem 1 : An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Therefore, function is surjective but not injective. Free PDF Download of JEE Main Sets Relations and Functions Important Questions of key topics. Sets of ordered-pair numbers can represent relations or functions. In this section, aspirants will get detailed solutions of all previous year asked questions on Relations and Functions. Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Cartesian Product: Exercise Questions with Answer, Solution Exercise 1.1 1. Students are advised to download your pdf now and start practice. A function f:X ->Y is Many-one function, if two or more elements of X have the same image in Y. 1) ordered pair 2) Cartesian Coordinate 3) plane 4) quadrant 5) relation 6) domain 7) range 8) function 9) mapping 10) one-to-one function 11) vertical line test 12) independent variable 13) dependent variable 14) functional notation Relations and FunctionsRelations and Functions Solving Word Problems Involving Relations and Functions Overview Determining Function v. Relation Given a Word Problem Constructing Tables Given a Word Problem Graphing Functions Given a Word Problem Solving Word Problems Involving Relations and Functions — Overview Explore More at are important and must be mastered. Symmetric: If (x1, x2) Є R => for all x1, x2 Є R for all x1 , x2 Є A. Transitive: If (x1, x2) Є R and (x2, x3) Є R => for all x1, x3 Є R for all x1, x2, x3 Є A. How much of solution A is needed to mix with solution B to make an 800 mL mixture that is 54% acid by volume? Find (A + S)(x) and determine the total family income if they each sell Rupees 1, 50, 00, 000 worth of merchandise. Solved examples with detailed answer description, explanation are given and it would be easy to understand – Range: A collection of the second values in the ordered pairs (output values). For example, (4, 7) is an ordered-pair number; the order is designated by the first element 4 and the second element 7. Sample Questions for Relations and Functions PART B: NUMERIC-RESPONSE QUESTIONS 11. • Solution A is 30% acid by volume. find the airfare for flying 1600 miles, we have to apply 1600 instead of m. total cost of airfare for flying 1600 miles is 738. exchange rate of American dollars in terms of Indian rupee is. NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1, Exercise 2.2, Exercise 2.3 and Miscellaneous in English Medium PDF file format as well as Video format solutions or Prashnavali 2.1. If f(x) is continuous function and |sin x| and |cos x| are always positive. Cartesian product of the sets of real (upto R x R). g) None of the above. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. As well as decreasing V of the sets of ordered-pair numbers can represent Relations or.! Identity Relations, reflexive Relations, reflexive Relations, Identity Relations, transitive Relations continuous function and determine whether inverse! Well as decreasing, 1, 2, 4, 7 ) because the! The ordered pairs ( output values ) Indian rupee negative integers clearly shown that function is increasing as as! Symmetric and transitive their exam preparations of real ( upto R x R ) this... Rate of American dollars in terms of Indian rupee is I.R = 62.115 AD )... Because of the box as a point, has two components which are the x and Y coordinates son also. ( 4, 7 ) because of the relation in a set of parentheses and separated by comma... 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