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Let F X 4 X 4 X 2 Then F X F 1 X Is Equal To

Solution: (2) f (x) = 4x / [4x + 2] f (1 - x) = 41-x / [y1-x + 2] = (4 / 4x) / ((4 / 4x) + 2) = 2 / [4x + 2] f (x) + f (1 - x) = [4x / [4x... View Article

If The Function F G H Are Defined From The Set Of Real Numbers R To R Such That F X X 2 1 G X Root X 2 1 H X 0 If X 0 X If X 0 Then Hofog X Is

Solution: (4) (hofog) (x) = h (f (g (x))) = h (f (√x2 + 1)) = h ((√x2 + 1)2 - 1) = h [x2 + 1 - 1] = h (x2) = x2... View Article

Let F X X Sin Pi X 1 Where X Denotes The Greatest Integer Function The Domain Of F Is

Solution: (3) f (x) = [x] sin [(π / [x + 1])] [x + 1] = 0 0 ≤ [x + 1] < 1 -1 ≤ x < 0 R ~ [-1, 0) Domain of f is x ∈ (− ∞, −1) ∪ [0, ∞).... View Article

If F X Sin 2 X Sin 2 X Pi 3 Cosx Cos X Pi 3 And G 5 4 1 Then Gof X Is Equal To

Solution: (2) f (x) = sin2x + sin2 (x + π / 3) + cos x cos(x + π/3) = sin2 x + [(1 / 2) sinx + (√3 / 2) cosx]2 + cos x [(1 / 2) cosx - (√3 /... View Article

F X Root Tanx Tanx Root 3 X Is Defined For

Solution: (3) tan x is defined if x ≠ nπ + (π / 2) --- (1) If tanx > 0, then |tanx| + tanx > 0 --- (2) If tanx ≤ 0, then |tanx| + tanx... View Article

F X Log Root X 4 Root 6 X Is Defined For

Solution: (3) f (x) = log (√x - 4 + √6 - x) For log a, a > 0 for defined value of log x x ∈ [4, 6]... View Article

If F X X 1 X 1 12 Then D F Is

1) R –{–1, 1} 2) [0, 1) 3) (– ∞, −1] ∪ [0, 1) 4) None of these Solution: (2) f (x) = [(x / (1 - |x|))]1/12 (x / (1 - |x|)) ≥ 0 If x... View Article

If F X Root X 1 X 3 X 4 X 4.5 Then D F Is

1) ( − ∞, 4] 2) [3, ∞) 3) ( –∞, 1] ∪ [3, 4] ∪ [4. 5, ∞) 4) [3, 4] ∪ [4. 5, ∞) Solution: (3) f (x) is defined if (x - 1) (x - 3) (x - 4) (x... View Article

If F X 1 X 1 Cos 1 2x 1 Tan 3x Then D F Is

1) {-1, 0, 1} 2) {nπ : n ∈ I} 3) {nπ / 3 : n ∈ I} 4) None of these Solution: (4) f (x) is not defined if So, (1) is wrong. |x| - 1 = 0... View Article

The Domain Of F X Cot 1 X Root X 2 X 2 X Belongs To R Is

Solution: (3) √x2 - [x2] > 0 x2 - [x]2 > 0 x ∈ I [x] = x x2 ∈ R - I x2 ≠ I x2 = R - {0, ± 1, ± 2, …. x2 = R - {0, 1, 2, …. x = R... View Article

Let F X 1 X X 2 1 X 2 X 0 Then F

Solution: (4) f (x + [1 / x]) = x2 + (1 / x2) + 2 - 2 = x2 + (1 / x2) + (2) (x2) (1 / x2) - 2 f (x + [1 / x]) = [x + (1 / x)]2 - 2 Put (x +... View Article

Given F X 1 1 X G X F F X And H X F F F X Then The Value Of F X G X H X Is

Solution: (1) f (x) = (1 / [1 - x]) g (x) = f (f (x)) h (x) = f (f (f (x))) g (x) = 1 / (1 - [1 / (1 - x)]) = [1 - x] / -x = [x - 1] / x... View Article

If F X X Root 1 X 2 Then Fofof X

Solution: (2) f (x) = [(x / √1 + x2)] [f (x)]2 = [(x2 / 1 + x2)] (fof) (x) = f (f (x)) = f (x) / √1 + [f (x)]2 = x / [(√1 + x2) (√1 + (x2... View Article

Let F X Sin Pi X And S X F X 0 Then S Doesnot Contain

Solution: (4) f (x) = sin (π / x) [As f (x) > 0] = [x : (π / x) ∈ ⋃ (2nπ + 1) π] ⊇ {x : x ∈ ⋃ [(1 / [2n + 1]), (1 / 2n)] Df ⊇ (1 / 3, 1 /... View Article

The Function F X Lambda Sinx Lambda 2 Cosx G Lambda Has Period Equal To Pi 2 If Lambda Is

Solution: (2) f (x) = λ |sinx| + λ2 |cosx| + g (λ) f (x) is a periodic function with period a f (x + a) = f (x) f (x + [π / 2]) = f (x) λ... View Article

The Inverse Of The Function Y Log A X Root X 2 1 A 0 A 1 Is

Solution: (4) y = loga (x + √x2 + 1) Let f (x) = y x = f-1 (y) (x + √x2 + 1) = ay (x - ay)2 = x2 + 1 x2 + a2y - 2xay = x2 + 1 a2y - 1... View Article

If F X Cos 1 X X 2 Root 1 1 Mod X 1 X 2 1 The Domain Of F X Is

Solution: f (x) = cos-1 (x - x2) + √(1 - [1 / |x|]) + 1 / [x2 - 1] f1 (x) = cos-1 (x - x2) x2 - x - 1 ≤ 0 x = -b ± [√b2 - 4ac] / 2a x = 1... View Article

The Domain Of The Function F X Log 10 Log 10 Log 10 Log 10 X N Times Is

Solution: (4) y = f (x) = log10 log10 log10…log10 x (n times) log10 log10 log10…log10 x > 0 log10 log10 log10…log10 x > 1 log10 log10... View Article

The Period Of F X 1 2 Sinx Cosx Sinx Cosx Is

Let F And G Be Functions Defined By F X X X 1 And G X X 1 X Then Fog 1 X

Solution: (1) (fog)-1 (x) = (g-1 o f-1) (x) Since, f (x) = x + 1 ,y = x + 1 xy + y = x x (1 - y) = y x = y / [1 - y] f-1 (y) = y / [1 -... View Article

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