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Show that the relation R in the set A of all the books in a library of a college,
|
|
1
|
510
|
April 10, 2019
|
|
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f
|
|
1
|
1765
|
April 1, 2019
|
|
Show that f : [–1, 1] → R, given by is one-one. Find the inverse of the function f : [–1, 1] → Range f
|
|
1
|
619
|
April 1, 2019
|
|
State with reason whether following functions have inverse (i) f : {1, 2, 3, 4} → {10} with
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1
|
567
|
April 1, 2019
|
|
If f(x) = (4x+3) / (6x-4). show that fof (x) = x, for all x ≠ 2/3. What is the inverse of f?
|
|
1
|
1217
|
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
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|
1
|
678
|
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)
|
|
1
|
768
|
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)}
|
|
1
|
1342
|
April 1, 2019
|
|
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by
|
|
1
|
1536
|
April 1, 2019
|
|
Let f : N → N be defined by State whether the function f is bijective. Justify your answer
|
|
1
|
887
|
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
|
|
1
|
776
|
April 1, 2019
|
|
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer
|
|
1
|
1311
|
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 one-one
|
|
1
|
1103
|
April 1, 2019
|
|
Show that the Signum Function f : R → R, given by is neither one-one nor onto
|
|
1
|
1213
|
March 30, 2019
|
|
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto
|
|
1
|
1591
|
March 30, 2019
|
|
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto
|
|
1
|
1496
|
March 30, 2019
|
|
Check the injectivity and surjectivity of the following functions: (i) *f* : **N → N** given by *f(x* ) = x2
|
|
1
|
1268
|
March 30, 2019
|
|
Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R* is the set of all non-zero real numbers
|
|
1
|
2325
|
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
|
|
1
|
1159
|
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
|
|
1
|
566
|
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}
|
|
1
|
1312
|
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},
|
|
1
|
821
|
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
|
|
1
|
998
|
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
|
|
1
|
747
|
March 30, 2019
|
|
Given an example of a relation. Which is (i) Symmetric but neither reflexive nor transitive
|
|
1
|
1427
|
March 30, 2019
|
|
Show that each of the relation R in the set A = { x ∈Z: 0≤x≤12}, A={x} given by
|
|
1
|
3043
|
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
|
|
1
|
1298
|
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):
|
|
1
|
740
|
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
|
|
1
|
1316
|
March 30, 2019
|
|
Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive
|
|
1
|
1643
|
March 30, 2019
|