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If F N N Defined By F X X 2 X 1 X Belongs To N Then F Is

Solution: (3) f (x) = x2 + x + 1 The discriminant D = 1 - 4 = -3 f ‘ (x) = 2x + 1 = 0 x = -1 / 2 The function is increasing. f (1) = 3, f... View Article

If R And C Denote The Set Of Real Numbers And Complex Numbers Respectively Then The Function F C R Defined By F Z Z Is

Solution: (4) f : C → R f (z) = |z| ∀ z ∈ C f (1) = |1| = 1 f (-1) = |-1| = 1 f (1) = f (-1) but 1 ≠ -1 Since there is an absence of... View Article

If N A 4 And N B 6 Then The Number Of One One Function From A To B Is

Solution: (4) Given that n (A) = 4 and n (B) = 6 n (B) > n (A) The function is one-one function. The number of one-one function mapping... View Article

On The Set Of Integers Z Define F Z Z As Then F Is

Question: . Solution: (3) f (2) = {2 / 2 = 0, 1, 2, 3, 4, 5…} Every odd value of n yields zero. So, it is a many-one function. f (n) =... View Article

If F X X 1 2 1 X Greater Or Equal To 1 Then Statement I The Set X F X F 1 X 0 1 Statement Ii F Is A Bijection

Solution: (3) Bijection = one-one + onto f (x) = (x + 1)2 - 1, x ≥ - 1 f’ (x) = 2 (x + 1) ≥ 0, for x ≥ - 1 f (x) is one-one. As the... View Article

For Real X If F X X 3 5x 1 Then

Solution: (3) f is one-one and onto R f (x) = x3 + 5x + 1 f '(x) = 3x2 + 5 > 0 ∀ x ∈ R. f(x) is strictly increasing on R⇒ f(x) is one-one... View Article

A 1 2 3 4 And B 1 2 3 4 5 6 Are Two Sets And Function F A B Is Defined By F X X 2 For All X Belongs To A Then The Function F Is

Solution: (3) At x = 1, f (x) = 3 At x = 2, f (x) = 4 At x = 3, f (x) = 5 At x = 4, f (x) = 6 f (x) is one-one but into since codomain ≠ range.... View Article

The Function F 0 Infinity 0 Infinity Defined By F X 2x 1 2x Is

Solution: (2) f is one-one function: f (x1) = f (x2) 2x1 / [1 + 2x1] = 2x2 / [1 + 2x2] 2x1 + 4x1x2 = 2x2 + 4x1x2 x1 = x2 f is not... View Article

The Total Number Of Injections One One And Into Mappings From A 1 A 2 A 3 A 4 To B 1 B 2 B 3 B 4 B 5 B 6 B 7 Is

Solution: (4) A = {a1, a2, a3, a4} B = {b1, b2, b3, b4, b5, b6, b7} n (A) = 4 and n (B) = 7 Total number of injections = 7P4 = 7! / 3!... View Article

The Function F 0 3 1 29 Defined By F X 2 X 3 15 X 2 36 X 1 Is

Solution: (2) f (x) = 2x3 - 15x2 + 36x + 1 f ‘ (x) = 6x2 - 30x + 36 = 6 (x - 2) (x - 3) f ‘ (x) > 0 f (x) is increasing in [0, 2) and... View Article

The Function F X X 2 Bx C Where B And C Are Real Constants Describes

Solution: (4) f (x) = x2 + bx + c It is a quadratic equation. The value of a is positive. The minimum value is (-b / 2a, -D / 4a). It is... View Article

If A 1 3 5 7 And B 1 2 3 4 5 6 7 8 Then The Number Of One One Function From A Into B Is

Solution: (5) Given: A ={1, 3, 5, 7}; B = {1, 2, 3, 4, 5, 6, 7, 8} n (A) = 4 and n (B) = 8 The number of one-one function from A into B is... View Article

If F N N Is Defined By Then F Is

Question: . Solution: (1) f : N → N is defined by f (1) = [1 + 1] / 2 = 1, f (2) = 2 / 2 = 1 f (1) = f (2) but 1 = 2 f (x) is not... View Article

X 2 X Y Is A Relation Which Is

Solution: Reflexive: xRx x2 = x . x Symmetric: (x, y) → x2 = xy (y, x) → y2 = xy It is not symmetric. Transitive: (x, y) (y, z) (x, z)... View Article

If R Is A Relation On The Set Of Integers Given By Arb A 2 K B For Some Integer K Then R Is

Solution: (1) aRB => a = 2k .b, k ∈ I Reflexive: (a, a) ∈ R k = 0, a = 20 b = b aRa Symmetric: If a = 2k .b then b = 2-kb where k, -k... View Article

Which Of The Following Statements Is Not Correct For The Relation R Defined By Arb If And Only If B Lives Within One Kilometre From A

Solution: (3) (a, a) ∈ R R is reflexive. (a, b) ∈ R ⇒ a lives within one kilometre from b ⇒b lives within one kilometre from a So, (a, b)... View Article

If W Denotes The Words In The English Dictionary Define The Relation R By R X Y W W Thewords X And Y Have At Least One Letter In Common Then R Is

Solution: (1) The given relation is R = {(x, y) ∈ W × W : the words x and y have at least one letter in common} Reflexive: (a, a) ∈ R If a... View Article

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