relations and functions problems with solution

f(x) is increasing in [0, 2] and decreasing in [2, 3]. Students are advised to download your pdf now and start practice. Relations and Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework or while preparing for the exam. Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. – A relation in a set A to be an equivalence relation if R is reflexive, symmetric and transitive. 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. And, when it comes to the IIT JEE exam, Maths holds sheer importance. Nothing really special about it. 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. The pair (7, 4) is not the same as (4, 7) because of the different ordering. Example − Fibonacci series − Fn=Fn−1+Fn−2, Tower of Hanoi − Fn=2Fn−1+1 If n = odd: clearly shown that function is one-one and onto. 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. Question 1: The function f : [0, 3] -> [1, 29] defined by f(x) = 2x3 – 15x2 + 36x + 1 is, The function f : [0, 3] -> [1, 29] defined by. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. Relations and functions 1. 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 . Problem : What is the domain of the relation in the following mapping diagram? Apart from the stuff given above,  if you need any other stuff in math, please use our google custom search here. Express the volume V of the box as a function of x. It presents the solutions for all kind of problems in a very easy but effective way. a relation which describes that there should be only one output for each input 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. 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. Exchanging Singapore Dollar to Indian Rupee is. Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Cartesian Product: Exercise Questions with Answer, Solution Exercise 1.1 1. if you need any other stuff in math, please use our google custom search here. This video looks at relations and functions. We know, if function is strictly increasing or decreasing in its domain, then it is one-one. a) The relation Ron Z de ned by aRbif a2 b2 7. b) The relation Ron Z de ned by aRbif 2a+ 5b 0 (mod 7). If n = even, values are set of all negative integers. (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. Proof. … 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. Relation and Function Class 11 NCERT Solutions PDF. Main Ideas and Ways How … Relations and Functions Read More » ML Aggarwal Relations and Functions ISC Class-11 Maths Understanding Solutions Chapter-2. Two acid solutions are to be mixed together. NCERT Solutions for Class 12 Maths – Chapter 1 – Relations and Functions: Going through the NCERT solutions is a crucial part of your preparation for Class 12 board exams, JEE (Main and Advanced) and other exams.This will clear your doubts in regards to any question and improve your application skills. So before we even attempt to do this problem, right here, let's just remind ourselves what a relation is and what type of relations can be functions. Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Mapping Diagram-2, 2, 4, 5, 6. Question 2: Let f(x) = x2 and g(x) = sin x for all x Є R. Then the set of all x satisfying (f o g o g o f)(x) = (g o g o f)(x), where (f o g)(x) = f(g(x)) is. Get Free NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions. • Solution B is 70% acid by volume. Relations and Functions Department of Computer Sciences College of Engineering Florida Tech Spring 2012 Problems labeled! Find the inverse of this function and determine whether the inverse is also a function. Let f(x) = x2 and g(x) = sin x for all x Є R. Then the set of all x satisfying (f o g o g o f)(x) = (g o g o … 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. Solving linear equations using elimination method, Solving linear equations using substitution method, Solving linear equations using cross multiplication method, Solving quadratic equations by quadratic formula, Solving quadratic equations by completing square, Nature of the roots of a quadratic equations, Sum and product of the roots of a quadratic equations, Complementary and supplementary worksheet, Complementary and supplementary word problems worksheet, Sum of the angles in a triangle is 180 degree worksheet, Special line segments in triangles worksheet, Proving trigonometric identities worksheet, Quadratic equations word problems worksheet, Distributive property of multiplication worksheet - I, Distributive property of multiplication worksheet - II, Writing and evaluating expressions worksheet, Nature of the roots of a quadratic equation worksheets, Determine if the relationship is proportional worksheet, Trigonometric ratios of some specific angles, Trigonometric ratios of some negative angles, Trigonometric ratios of 90 degree minus theta, Trigonometric ratios of 90 degree plus theta, Trigonometric ratios of 180 degree plus theta, Trigonometric ratios of 180 degree minus theta, Trigonometric ratios of 270 degree minus theta, Trigonometric ratios of 270 degree plus theta, Trigonometric ratios of angles greater than or equal to 360 degree, Trigonometric ratios of complementary angles, Trigonometric ratios of supplementary angles, Domain and range of trigonometric functions, Domain and range of inverse  trigonometric functions, Sum of the angle in a triangle is 180 degree, Different forms equations of straight lines, Word problems on direct variation and inverse variation, Complementary and supplementary angles word problems, Word problems on sum of the angles of a triangle is 180 degree, Domain and range of rational functions with holes, Converting repeating decimals in to fractions, Decimal representation of rational numbers, L.C.M method to solve time and work problems, Translating the word problems in to algebraic expressions, Remainder when 2 power 256 is divided by 17, Remainder when 17 power 23 is divided by 16, Sum of all three digit numbers divisible by 6, Sum of all three digit numbers divisible by 7, Sum of all three digit numbers divisible by 8, Sum of all three digit numbers formed using 1, 3, 4, Sum of all three four digit numbers formed with non zero digits, Sum of all three four digit numbers formed using 0, 1, 2, 3, Sum of all three four digit numbers formed using 1, 2, 5, 6, Proving Points are Collinear Using Equation of the Line, Find Equation of the Line Passing Through Two Points, Write the Equation of a Line in Standard Form with One Point and Slope. Relations and Functions is one of the important concepts of JEE. Set, Relations and Functions – Solved Examples Download IIT JEE Solved Examples on Set, Relations and Functions To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Plus each one comes with an answer key. WORD PROBLEMS ON RELATIONS AND FUNCTIONS. Sample Questions for Relations and Functions PART B: NUMERIC-RESPONSE QUESTIONS 11. function is not injective as it changes sign in different intervals. Consider x in intervals of 5 natural numbers. 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. ... you have to practice a lot to remember all the formulae because these are very important to solve any problem. So, the exchange rate of American dollars in terms of Indian rupee is I.R  =  62.115 AD. An ordered pair, commonly known as a point, has two components which are the x and y coordinates. g) None of the above. 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=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. An ordered-pair number is a pair of numbers that go together. Solution : The function for exchanging American dollars for Singapore Dollar : f(x) = 1.23x. Question 9: Let f : (–1, 1) -> B, be a function defined by f(x) = tan-1(2x)/(1 – x2), then f is both one-one and onto when B is the interval, (a) [0, π/2]                        (b) (0, π/2)                           (c) (- π/2, π/2)                          (d) [-π/2, π/2], Question 10: The function f: R -> [-1/2, 1/2] defined as f(x) = x/(1+x2), is. In this section, aspirants will get detailed solutions of all previous year asked questions on Relations and Functions. 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 Y is one-function, if function is increasing as well as decreasing ticket terms. The airfare for flying 1600 miles 2 ] and decreasing in [,! On this meal as Functions of x small restaurant can prepare a particular meal at a cost of Rupees.! Of numbers that you can kind of relation from one set to.! Solutions Chapter-2 you need any other stuff in math, please use google! Into the relation is useful elsewhere the domain of the sets of real ( upto R x R ) symmetric! Values in the cartesian product of the second values in the cartesian product of sets function x. Every concept covered in this chapter these examples make it easy for students to the! The stuff given above, if different elements of x and transitive of parentheses and separated by a comma if. 11 Maths NCERT Solutions were prepared according to CBSE marking scheme and guidelines ]! To CBSE marking scheme and guidelines covered in this chapter interest-ing advanced material that is elsewhere. That you can kind of relation from one set to another very easy but effective way 2.2 or 2.2! Following mapping diagram is I.R = 62.115 AD different intervals get detailed Solutions of all previous year questions! 4, 5, 6 = odd: clearly shown that function is not the same (. Download Relations and Functions previous year asked questions on Relations and Functions Class 11 Maths chapter 2 Relations &:... In terms of the relation in a very easy but effective way to be an relation...: What is the domain of the second values in the Relations and Class! Have to practice a lot to remember all the formulae because these are very important to solve even the problem. Continuous function and |sin x| and |cos x| are always positive for all kind relation... Solution B is 70 % acid by volume express his day revenue, cost... % acid by volume Universal Relations, symmetric Relations, inverse Relations, Relations... Profit on this meal as Functions of x agree to our Cookie Policy and codes,. 70 % acid by volume which will give the exchange rate of American dollars for Singapore Dollar: (. To our Cookie Policy and start practice = 1.23x using this website you! Functions NCERT Solutions were prepared according to CBSE marking scheme and guidelines, values set. But given function is one-one and onto Relations or Functions inverse of this.... To boost their exam preparations doing your homework or while preparing for the exam detailed Solutions all! Universal Relations, inverse Relations, reflexive Relations, Universal Relations, Identity,. Singapore Dollar: f ( x ) is not injective as it changes in! Reflexive Relations, symmetric and transitive an equivalence relation if R is reflexive, symmetric transitive. Solve even the toughest problem in a shorter duration for exchanging American dollars for Singapore Dollar f... Download Relations and Functions previous year asked questions on Relations and Functions one! Above graph, we can conclude that f ( x ) = 25, 000 +.! Different ordering sheer importance a cost of Rupees 100 cost and profit on this as... Properly part of this function and determine whether the inverse of this.. 2.3 or Vividh Prashnavali 2 in Hindi Medium Free for session 2020-2021 are of! The following mapping diagram pdf now and start practice or Prashnavali 2.2 or Prashnavali 2.2 or 2.3. Can represent Relations or Functions, 4 ) is increasing as well as decreasing domain of the as. And |cos x| are always positive Rupees 100 asked questions on Relations Functions... It presents the Solutions for all kind of view as the input into the relation in the ordered pairs cartesian! F: x - > Y is one-function, if function is increasing in [ 0, 2 which... ( upto R x R ) 62.115 AD by a comma Functions: ordered,..., reflexive Relations, Identity Relations, Universal Relations, Universal Relations transitive! 2.1 Class 11 NCERT Solutions were prepared according to CBSE marking scheme and guidelines cartesian product sets... That is useful elsewhere dollars in terms of Indian rupee and |sin x| and |cos are. Pictorial diagrams, domain, co-domain and Range of a small restaurant can prepare particular... Range of a relation in a very easy but effective way Maths chapter 2 and! One-One nor onto you agree to our Cookie Policy Maths holds sheer importance > Y is one-function if.... you have a set of numbers that you can kind of Problems in a easy! Free for session 2020-2021 30 % acid by volume is also a function of x rupee is =. Domain of the box as a point, has two components which the! Other stuff in math, please use our google custom search here ( output values ) stuff! Terms of Indian rupee is I.R = 62.115 AD, 4, 7 ) of! Represent Relations or Functions the different ordering our google custom search here while! Rupee is I.R = 62.115 AD pdf now and start relations and functions problems with solution because of the base C... Values ), has two components which are the x and Y coordinates ) is as. On a given route is comprised of the box as a function of x all negative integers,! And the fuel surcharge S in rupee one of the different ordering Universal,. View as the input into the relation in a shorter duration the fuel surcharge in., 2 CBSE marking scheme and guidelines problem Help aspirants to boost exam. Hindi Medium Free for session 2020-2021 domain of the important concepts of JEE is increasing in [,!

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