Show that the relation R in the set A of all the books in a library of a college,


2

85

April 10, 2019

Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f


2

306

April 1, 2019

Show that f : [–1, 1] → R, given by is oneone. Find the inverse of the function f : [–1, 1] → Range f


2

144

April 1, 2019

State with reason whether following functions have inverse (i) f : {1, 2, 3, 4} → {10} with


2

92

April 1, 2019

If f(x) = (4x+3) / (6x4). show that fof (x) = x, for all x ≠ 2/3. What is the inverse of f?


2

290

April 1, 2019

Find gof and fog, if (i) f(x) =  x  and g(x) =  5x – 2  (ii) f(x) = 8x3 and g(x) = x1/3


2

119

April 1, 2019

Let f, g and h be functions from R to R. Show that (f + g)oh = foh + goh (f . g)oh = (foh) . (goh)


2

211

April 1, 2019

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)}


2

463

April 1, 2019

Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by


2

92

April 1, 2019

Let f : N → N be defined by State whether the function f is bijective. Justify your answer


2

164

April 1, 2019

Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function


2

128

April 1, 2019

In each of the following cases, state whether the function is oneone, onto or bijective. Justify your answer


2

247

April 1, 2019

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is oneone


2

363

April 1, 2019

Show that the Signum Function f : R → R, given by is neither oneone nor onto


2

295

March 30, 2019

Show that the Modulus Function f : R → R, given by f(x) = x, is neither oneone nor onto


2

282

March 30, 2019

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither oneone nor onto


2

325

March 30, 2019

Check the injectivity and surjectivity of the following functions: (i) *f* : **N → N** given by *f(x* ) = x2


2

171

March 30, 2019

Show that the function f : R* → R* defined by f(x) = 1/x is oneone and onto,where R* is the set of all nonzero real numbers


2

192

March 30, 2019

Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer


2

146

March 30, 2019

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer


2

129

March 30, 2019

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}


2

193

March 30, 2019

Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides},


2

181

March 30, 2019

Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation


2

166

March 30, 2019

Show that the relation R in the set A of points in a plane given by R = {(P, Q): distance of the point P


2

195

March 30, 2019

Given an example of a relation. Which is (i) Symmetric but neither reflexive nor transitive


2

245

March 30, 2019

Show that each of the relation R in the set A = { x ∈Z: 0≤x≤12}, A={x} given by


2

959

March 30, 2019

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = { (a,b) ; a  b is even}, is an equivalence relation


2

246

March 30, 2019

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y):


2

100

March 30, 2019

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive


2

215

March 30, 2019

Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive


2

220

March 30, 2019
