Class XII ISC Maths Chapter Relation and Functions Exercise 1.3
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class 12 relation&function exercise1-1
Relations & Functions
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Q1 Let A= {1, 2} B= {3, 6}, function f: A -> B be defined by f(x) = 3x and function g: A → B be defined by g(x) = x2 + 2. Show that f = g
Q2 Check the injectivity and surjectivity of the following functions
(i) f: N→N defined by f(x) = x2
(ii) f: Z →Z defined by f(x) = x2
(iii) f: R→R defined by f(x) = x2
(iv) f: N→Q defined by f(x) = x3
(v) f:Z →Z defined by f(x) = x3
(vi) f:R→R defined by f(x) = x3
Q3 Let I be the set of all integers, Show that the function f: I→I defined by f(x)=|x| is neither one-one nor onto.
Q5 let A= {1, 2, 3},B= (4, 5, 6, 7} and f: {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one but not onto.
Q6 In each of the following cases state whether the function is bijective or not. Justify your answer
(i) f: R →R defined by f(x) = 2x + 1
(ii) f: R → R defined by f(x) = 3 - 4x
(iii) f : R→R defined by f(x) =1 + x2
Q8 Let A = R — {2} and B= R - {1}. Show that the function fi A → B defined by f(x)= x-1 / x-2 is bijective.
Q9 Show that the function f : R -> R defined by f(x) = cos x iS neither one-one nor onto
Q10 Show that the function f: I→I defined by f(x) = x2 + x is neither one-one nor onto .
Q11 If the function f: I -> I is defined by
find,
(i) f (3)
(ii) f (4)
(iii) x, if f(x) = -9.
Is this function one-one?
find,
Q17 Is the function f : N —> N defined by f(m) = m2 + m + 2 one-one? Justify your answer.
Q21 Find the range of the following functions :
(i) f (x) = sin x + cos x
(ii) f(x) = 3 sin x + 4 cos x.
Q22 The function f: R -> R is defined by f(x) = |2x -3|.
(i) Is f one-one?
(ii) Is f onto?
Q24 If A = {a, b, c} and B = {1, 2, 3, 4}, then find the number of functions from A to B.
Q25 If A = {a, b} and B = {1, 3, 5}, then find the number of one-one functions from A to B.
Q26 If A = {a, b, c} and B = {p, q}, then find the number of onto functions from A to B.
Q27 If A = {1, 2, 3, 4} and B = {-1, 3}, then find the number of onto functions from A to B.
Q28 If A = {1, 2, 3} and B = {a, B, c}, then find the number of one-one onto functions from A to B.
Q29 If A = {1, 2, 3, 4} and B = {a, b, c}, then find the number of bijections from A to B.
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