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If F X 1 F X 1 Root 3 F X For All X Belongs To R Then The Period Of F X Is

Solution: (3) If f (x) is periodic with period p, f (x + p) = f (x) f (x + 1) + f (x - 1) = √3 f (x) f (x + 1) = √3 f (x) - f (x - 1) When... View Article

The Period Of F X 10 Cos 2 Pi X X X Sin 2 Pi X Is

The period of f (x) =is 1) 1 2) 2 3) 3 4) π Solution: (1) f (x) = cos2 π (x + 1) = cos2 (πx + π) and x + 1 - [x + 1] = x - [x] f (x +... View Article

The Period Of The Function F X Cos X 2 Sinx Is

Let F X X 2 0 X 2 2x 3 2 X 3 X 2 X 3 Then

Let f (x) = x2, 0 < x < 2 = 2x – 3, 2 ≤ x < 3 = x + 2, x ≥ 3. Then 1) 2) 3) 4) Solution: (1) f (3 / 2) = 9 / 4 as (3 / 2) <... View Article

Let F X 4 Cos Root X 2 Pi 2 9 Then

1) Df = [π / 3, ∞), Rf = [-1, 1] 2) Df = [π / 3, ∞), Rf = [-2, 2] 3) Df = (- ∞, - π / 3] ⋃ [π / 4, ∞) 4) Df = (-∞, π / 3), Rf = (0, 4]... View Article

If E X E F X E Then For F X

Solution: (3) ex + ef(x) = e ex + ey = e ex = e - ey x = log (e - ey) e - ey > 0 ey < 0 y < 1 y ∈ (−∞, 1)... View Article

If F X And G X Are Two Functions Of X Such That F X G X E X And F X G X E X Then

Solution: (3) f (x) + g (x) = ex f (x) − g (x) = e–x Add the above equations, 2 f (x) = ex + e-x f (x) = [ex + e-x] / 2 Put f (x)... View Article

Let F Infinity 1 Infinity 1 Such That F X X 2 X Then F 1 X Is

Solution: (2) y = f (x) = x (2 − x) = 2x - x2 x2 - 2x + y = 0 x = 2 ± [√4 - 4y] / 2 = 1 ± √1 - y Since, x ≤ 1, x = 1 - √1 - y f-1 (y)... View Article

F X 1 1 X X 0 1 Then The Graph Of The Function Y F F F X X 1 Is

Solution: (3) f (x) = 1 / (1 - x) f (f (x)) = 1 / [1 - f (x)] = (1 - x) / (-x) = [x - 1] / x y = f ( f (f (x)) = 1 / [1 - {(x - 1) / x}]... View Article

Let F X Be A Function Whose Domain Is 5 7 Let G X 2x 5 Then Domain Of Fog X Is

Solution: (3) g(x) = | 2x + 5 | Domain of f (x) = [-5, 7] -5 ≤ |2x + 5| ≤ 7 |2x + 5| is positive. |2x + 5| ≤ 7 -7 ≤ 2x + 5 ≤ 7 -12 ≤ 2x... View Article

The Range Of The Function F X X 1 X 2 1 X 3 Is

Solution: (2) For -1 ≤ x ≤ 1, f (x) = - (x - 1) - (x - 2) For 1 ≤ x ≤ 2, f (x) = (x - 1) - (x - 2) = 1 For 2 ≤ x ≤ 3, f (x) = 2x - 3 x ∈... View Article

If F X Sin 1 Root X 4 Then The Range Of X Is

Solution: (1) f (x) = sin-1 √x - 4 (x - 4) = sin2 [f (x)] 0 ≤ (x - 4) ≤ 1 4 ≤ x ≤ 5 Range = [4, 5]... View Article

The Domain Of The Function F X Root Log 0.3 X 1 Root X 2 2x 8 Is

Solution: (3) -log0.3 (x - 1) ≥ 0, (x - 4) (x + 2) < 0 (x - 1) > 0 and x ≠ -2, 4 x ≥ 2, -2 < x < 4, x > 1, x ≠ -2, 4 x ∈ [2,... View Article

If Q X M X L M L L X M L M Then Q L Q M Is Equal To

Solution: (2) Q (l) + Q (m) = m . 0 + l [(l - m) / (l - m)] + m . [(m - l) / (m - l)] + l . 0 = l .1 + m .1 = l + m Q (l + m1) = (m / (m -... View Article

If The Function F R R Be Such That F X X X Where X Denotes The Greatest Integer Less Than Or Equal To X Then F 1 X Is

Solution: (3) f (x) = x − [x] The greatest integer function is [x]. For different values of x, the same values of the function exist.... View Article

Let F R R Be A Function Defined By F X E X E X E X E X Then

Solution: (4) Let f (x) = f (y) [e2x - 1] / [e2x + 1] = [e2y - 1] / [e2y + 1] 2e2x = 2e2y e2(x-y) = 0 It is not injective. Let y =... View Article

Let F Be A Function 2 F X Y F X Y F Y X And F 1 P 1 Then P 1 Sum Of R 1 N F R

1) p (pn - 1) / (p - 1) 2) pn / (p - 1) 3) (pn + 1) / (p + 1) 4) pn+1 - p Solution:(4) 2 f (x, y) = [f (x)]y + [f (y)]x Put y = 1, 2 f... View Article

If F X Is A Polynomial Satisfying F X F 1 X F X F 1 X And F 3 28 Then F 4 Is Given By

Solution: (3) f (x) = xn + 1 f (3) = 33 + 1 = 28 3n = 27 n = 3 f (4) = 43 + 1 = 65... View Article

If F 2x Y 8 2x Y 8 Xy Then F X Y F Y X

Solution: (2) f (2x + (y / 8), 2x - (y / 8)) = xy Put h = 2x + (y / 8) and k = 2x - (y / 8) x = (1 / 2) (h + k) and y = 4 (h - k) f (h, k)... View Article

If A F X Bf 1 X X 1 X 0 And A B Then F 2

Solution: a f (x) + bf (1 / x) = x - 1 (i) at x = 2, a f (2) + bf (1 / 2) = 2 - 1 = 1 --- (1) * a (ii) at x = 1 / 2, a f (1 / 2) + bf (2) =... View Article

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