👉 🔥 CLICK HERE! 🔥 👈

Youre Reading a Free Preview Pages 6 to 13 are not shown in this preview. Live worksheets > English > Math > Functions > Relations and Functions Finish!! Please allow access to the microphone Look at the top of your web browser. If you see a message asking for permission to access the microphone, please allow. Close (a) The Cartesian product $P times P$ has 9 elements among which are found (-2, 0) and (0, 2). the set P is _____ and the remaining elements of P × P__________(b) The function f(x) is defined as $x^2$ . The value of $ frac f(2) -f(1)2-1$ ______(c) The function p(x)=x+1 and q(x)=2x-1.The value (fg)x is ______(d) The Function g(x)=6x2+3x-2 The value of g(-1) is ________Solutiona. Since n(P × P) =9, Set P has three elements. Now since (–2, 0) and (0, 2) belongs P × P, Set P =-2,0,2Remaining elements in P × P are (-2,-2),(-2,2),(0,-2),(0,0),(2,-2),(2,0),(2,2)b. 3c. $frac x+12x -1$d. $g(-1) = 6 (-1)^2 + 3 (-1) -2 =1$ (1) The relation defined as (2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1) is a function(2) The relation defined as (2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7) is not a function(3) The relation defined as (1, 3), (1, 5), (2, 5) is a function(4) The below graph is not a function(5) A function are relations but all relations are not functions(6) A function is defined as$f(x) =- sqrt -2x+5$The domain is x≤ 52 and Range is f(x) ≤ 0(7) P= 1,2,3 Q=e,f. The total number of relation from P × Q is 64(8) The below graph is a function(9) The below graph is not a function(10) The ordered pair (x,y)|y < 3x+1 is a function(11) The ordered pair (x,y)|y=x2 is a relation but not function(12) The ordered pair (x,y)| x=3 and y is real number is a relation and functionSolution Find the domain and range of the following real function:(1) $y=x^2$(2) $y=-|x|$(3) $y=3x-7$(4) $y=-x^4 + 3$(5) $y= sqrt 2-x$(6) $y =frac 1 sqrt 11-x$Solution1. $y=x^2$Domain is all the Real number as function is defined for all valuesDomain =RThe function always provides positive value. So range is $0,infty)$ 2.$y=-|x|$Domain is all the Real number as function is defined for all valuesDomain =RThe function always provides negative value. So range is $(-infty,0$ 3.$y=3x-7$Domain is all the Real number as function is defined for all valuesDomain =RThe is a linear function. Range is also R 4.$y=-x^4 + 3$Domain is all the Real number as function is defined for all valuesDomain =RNow it can be written as$y=3 -x^4$Now $x^4$ will always be positive for all real values of x,So Range will be $(-infty,3$ 5. $y= sqrt 2-x$Now this function is defined for x where $2 -x geq 0$or $ x leq 2 $So Domain is $ (-infty,2 $ Since square root gives positive values only, Range is $0,infty)$ 6.$y =frac 1 sqrt 11-x$Now this function is defined for x where $11 -x > 0$ as or $ x < 11$So Domain is $(-infty,11)$Since square root gives positive values only.Also this function cannot have zero value, So Range is $(0,infty)$ If A= 1,2,3, 5, 7, 9, 11, B = 7, 9, 11, 13, C = 11, 13, 15 D = 17,19,21,23 and E=1,-1 find(i) What is the number of element in $A times B$(ii) How many number of relations can be found from $A times C$(iii) The mapping defined as (1,11),1,13,2,7,5,11 is a function from A × B,State True or False(iv) The mapping defined as (11,17),(13,19),(15,21),(15,23) is a Relation from C × D, State True or False(v) Find the value of B × C and C × B(vi) Find the value of E × E × E(vii) Verify that A × (B ∩ C) = (A × B) ∩ (A × C)(viii) A X B is a subset of A X C. State True or false(ix) (A X B) ∩ (B ∪ D)Solutioni. n(A)=7 ,n(B)=4, $n(A times B)=28$ii. n(C) =3. Number of relation from A to C = $2^21$iii. False as one elements is mapping to two elementsiv. Truev. $B times C= (7,11),(7,13),(7,15) ,(9,11),(9,13),(9,15),(11,11),(11,13),(11,15),(13,11),(13,13),(13,15)$$C times B= (11,7),(11,9),(11,11) ,(11,13),(13,7),(13,9),(13,11) ,(13,13),(15,7),(15,9),(15,11) ,(15,13)$ 1. Given the relation R = (6,4), (8,-1), (x,7), (-3,-6). Which of the following values for x will make relation R a function?(a) 8(b) 6(c) -3(d) 1SolutionSolution (d)2. Let n (A) = m, and n (B) = n. Then the total number of non-empty relations that can be defined from A to B is(a) $m^n$(b) mn- 1(c) $2^mn -1$(d) $n^m -1$SolutionSolution (c)3. The domain and range of real function f defined by f (x) = $sqrt x −1$ is given by(A) Domain = (1, ∞), Range = (0, ∞)(B) Domain = 1, ∞), Range = (0, ∞)(C) Domain = 1, ∞), Range = 0, ∞)(D) Domain = 1, ∞), Range = 0, ∞)SolutionSolution (c)4. If $f (x) = x^3 - frac 1x^3$ then $ f (x) + f(frac 1x)$(a) 0(b) $2x^3$(c) 1(d) $frac 2x^3$Solution$f (x) = x^3 - frac 1x^3$$f(frac 1x)) = frac 1x^3 - x^3$$ f (x) + f(frac 1x) = x^3 - frac 1x^3 + frac 1x^3 - x^3=0$ 1. What is the domain and range in the relation shown in below mappingSolutionDomain =-2,2,4,5,6Range=4,16,25,362. Please tell if the below mapping is function or notSolutionThis is not function There are two functions defined as belowLet P=(0,5),(1,4),(2,3),(3,2),(4,1),(5,0)Q=(1,1),(2,4),(3,9),(4,16),(5,25),(6,36)1.What is the domain and range of P2.What is the domain and range of Q3. What is the domain of function (Q-P)4. List the ordered pair of (Q-P) in set notation5. What is the domain of QP6. List the ordered pair of (QP) in set notationSolution1. Domain of P =0,1,2,3,4,5Range of P =5,4,3,2,1,02. Domain of Q =1,2,3,4,5,6Range of P =1,4,9,16,25,363. The domain of function (Q-P) is the intersection of domain of P and QSo, Domain of (Q-P)=1,2,3,4,54.(1,-3),( 2,1),(3,7),(4,15),(25)5. The domain for QP is 1,2,3,4 as on 5 function p is zero6. The ordered pair of QP(1,14),(2,43),(3,92),(4,16)Download Relations and functions class 11 Worksheets as pdf Also Read
https://wakelet.com/wake/vAN1q935JoV0-DUPIEk8Y
https://sazinuje.weebly.com/uploads/1/3/4/5/134588850/sitexuke-rerejeropojol.pdf
https://wakelet.com/wake/_UYzgHR6i64T7BvlZUOnM
https://wakelet.com/wake/DbdAc6y7Dli_vmpult2i0
https://wakelet.com/wake/dG4MkpEjPkJIGKuEmy-yE
http://lanhcongnghiepthinhphat.com/upload/files/36199698654.pdf
https://wakelet.com/wake/fQ72y90dZE_WrVKkKL0cv
https://wakelet.com/wake/apqykDP25aqa1ML0tdXlp
https://wakelet.com/wake/vaYxBtSxG0KExXGzkdRCM
https://birivuben.weebly.com/uploads/1/3/4/6/134618962/purevi.pdf
https://wakelet.com/wake/nh9W7pHWvLF4KNW8hVdQd
https://wakelet.com/wake/cXV-ZLNhYx-ivwUQE8B40
https://wakelet.com/wake/HHmbrlANPeJrL1RnpbLpb
https://wakelet.com/wake/Sq1A-OgUZTJdViGMAzEha
http://a899.net/userfiles/file/kotevejuvunojadomunonenun.pdf
https://kinhdoanhvaphapluat.com/img-dn/files/67202478642.pdf
http://global-gypsum.com/wp-content/plugins/formcraft/file-upload/server/content/files/162f3314bf1789---42344462606.pdf
https://wakelet.com/wake/wGunNfMSJiEByz_oMO30i
https://wakelet.com/wake/2-5wGERdWZIUvTCihfFOX

Items