The detailed step by step explanations provided for each problem help aspirants to solve even the toughest problem in a shorter duration. Students are advised to download your pdf now and start practice. Question 2: Let D be the domain of real valued function f defined by then, write D. Solution: Here given D is the domain of Therefore, Therefore, D = [– 5, 5] - Answer . Solution : (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. f(x) is increasing in [0, 2] and decreasing in [2, 3]. so, f(x) = f(y) => (x-1)/2 = (y-1)/2 => x = y, Question 4: The range of the function f(x) = 3|sin x| – 2|cos x| is. The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Cartesian product of the sets of real (upto R x R). We call that the domain. • Solution A is 30% acid by volume. A function f:X ->Y is Many-one function, if two or more elements of X have the same image in Y. A recurrence relation is an equation that recursively defines a sequence where the next term is a function of the previous terms (Expressing Fn as some combination of Fi with i 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=1n​f(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=1n​f(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. The pair (7, 4) is not the same as (4, 7) because of the different ordering. The answer is (e). Nothing really special about it. Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Cartesian Product: Exercise Questions with Answer, Solution Exercise 1.1 1. 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 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. Again, function is one-one and onto. Function as a special kind of relation from one set to another. WORD PROBLEMS ON RELATIONS AND FUNCTIONS. So, the exchange rate of American dollars in terms of Indian rupee is I.R  =  62.115 AD. Detailed solutions are also presented. He estimates that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is given by the function D(x) = 200−x. Find functional values. A simple cipher takes a number and codes it, using the function f(x) = 3x−4. Solution to Question 5: (f + g)(x) is defined as follows (f + g)(x) = f(x) + g(x) = (- 7 x - 5) + (10 x - 12) Group like terms to obtain (f + g)(x) = 3 x - 17 It presents the solutions for all kind of problems in a very easy but effective way. Express the volume V of the box as a function of x. The function for exchanging American dollars for Singapore Dollar : Here "x" stands for American dollar and f(x) stands for Singapore dollar. On the same day the function for exchanging Singapore Dollar to Indian Rupee is g(y) = 50.50y, where y represents the number of Singapore dollars. Relations and Functions; Problems; Domain; Problems; Range; Problems; Terms; Writing Help. Chapter 2 Relations & Functions: Ordered pairs, Cartesian product of sets. ML Aggarwal Relations and Functions ISC Class-11 Maths Understanding Solutions Chapter-2. Analyze and graph relations. if you need any other stuff in math, please use our google custom search here. This is the Aptitude Questions & Answers section on & Sets, Relations and Functions& with explanation for various interview, competitive examination and entrance test. If n = odd: clearly shown that function is one-one and onto. Free PDF Download of JEE Main Sets Relations and Functions Important Questions of key topics. Problem : What is the domain of the relation in the following mapping diagram? Here, the important concepts covered such as, increasing and decreasing of functions, type of functions, combination of functions, domain, range and more. 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. 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