Archives

The Period Of The Function F X Sin 4x Cos 4x Is

Solution: (2) f (x) = sin4x + cos4x = (sin2 x + cos2 x)2 - 2 sin2 x cos2 x = 1 - (4 / 2) sin2 x cos2 x = 1 - [2 sin cosx]2 / 2 = 1 - [sin2... View Article

The Domain Of The Function F X Exp Root 5x 3 2x 2 Is

Solution: (4) f (x) = exp (√5x - 3 - 2x2) 5x - 3 - 2x2 ≥ 0 -2x2 + 5x - 3 ≥ 0 x = - 5 ± [√25 - 4 (-2) (-3)] / [2 * -2] = [- 5 ± √25 - 24] /... View Article

The Largest Possible Set Of Real Numbers Which Can Be The Domain Of F X Root 1 1 X Is

Solution: (4) [x - 1] / x ≥ 0 ⇒ x ≥ 1 and x = 0 Domain is (-∞, 0 ) ∪ [1, ∞)... View Article

The Domain Of The Real Valued Function F X Root 5 4x X 2 X 2 Log X 4 Is

Solution: f (x) = √5 - 4x - x2 + x2 log (x + 4) log a ⇒ a > 0 √a ⇒ a ≥ 0 log (x + 4) ⇒ x + 4 > 0 x > -4 5 - 4x - x2 ⇒ -x2 - 4x... View Article

The Domain Of The Function F X Cos 1 X Is

Solution: (2) f (x) = cos-1 x The domain of f (x) is the same as the range of values of x. The range of cosx is [-1, 1]. The domain of f... View Article

If The Function F R R Defined By F X X Where X Is The Greatest Integer Not Exceeding X For X Belongs To R Then F Is

Solution: (3) The given function is not differentiable at x ∈ I, neither it satisfies for the even and odd function. Hence, the function is... View Article

The Period Of The Function F X Mod Sin X Mod Cos X Is

Solution: (2) f (x) = |sin x| + |cos x| The period of sinx is π and cosx is π. The given function is an even function and sinx, cosx is... View Article

If F R R And Is Defined By F X 1 2 Cos 3x For Each X Belongs To R Then The Range Of F Is

Solution: (2) f (x) = 1 / [2 - cos 3x] 2 - cos 3x ≠ 0 cos 3x ≠ 2 Domain: x ∈ R -1 ≤ cos 3x ≤ 1 1 ≥ -cos 3x ≥ -1 3 ≥ 2 - cos 3x ≥ 1 (1 /... View Article

The Domain Of The Function F X Root 4 X 2 Sin 1 2 X Is

Solution: (3) f (x) = √4 - x2 / sin-1 (2 - x) Consider √4 - x2 > 0 4 - x2 ≥ 0 (2 - x) (2 + x) ≥ 0 (2 + x) (x - 2) ≤ 0 x ∈ [-2, 2] --... View Article

The Domain Of The Function F X Sin 1 X 3 Root 9 X 2 Is

Solution: (1) f (x) = sin-1 (x - 3) / √9 - x2 Consider sin-1 (x - 3) -1 ≤ (x - 3) ≤ 1 2 ≤ x ≤ 4 9 - x2 > 0 x2 < 9 -3 < x <... View Article

If F R S Defined By F X Sin X Root 3 Cos X 1 Is Onto Then The Interval Of S Is

Solution: (4) f (x) = sin x -√3 cos x + 1 -√a2 + b2 ≤ a cos θ + b sin θ ≤ √a2 + b2 -2 ≤ sinx - √3 cosx ≤ 2 -1 ≤ sinx - √3 cosx + 1 ≤ 3... View Article

The Range Of F X Cos X Sin X Is

Solution: (4) f (x) = cos x - sin x = √2 [cosx (1 / √2) - sinx (1 / √2)] = √2 [cosx * cos (π / 4) - sinx * sin (√ / 4)] = √2 [cos (x + [π... View Article

The Domain Of The Function Sin 1 Log 2 X 2 2 Is

Solution: (2) f (x) = sin-1 (log2 [x2 / 2]) -1 ≤ (log2 [x2 / 2]) ≤ 1 -1 ≤ (log2 [x2 / 2]) < 2 (log2 [x2 / 2]) < 2 [x2 / 2] 22 [x2... View Article

The Domain Of The Function F X Log 10 Root X 4 Root 6 X Is

Solution: (1) f (x) = log10 (√x - 4 + √6 - x) If loga is present, then a > 0 for defined value of a. Put x = 4 it becomes log (0 + √2)... View Article

The Period Of The Function F X Sin Sin X 5 Is

Solution: (3) f (x) = sin (sin [x / 5]) The period of sinx is 2π. sin [sin (x + 2π) / 5] 2π = T / 5 T = 10π... View Article

The Period Of The Function F X A Tan Pi X X Where A 0 Pi Denotes The Greatest Integer Function And X Is A Real Number Is Defined As

Solution: (5) f (x) = a{tan (π) + x - |x|} = atanπx ax Period of f (x) is 1.... View Article

If F R R Is Defined By F X 2x 2 X For All X Belongs To R Where X Is The Greatest Integer Not Exceeding X Then The Range Of F Is

Solution: (2) f : R → R [2x] = [x] + [x + (1 / 2)] f (x) = [2x] - 2[x] = [x] + [x + (1 / 2)] - 2[x] f (x) = [x + (1 / 2)] - [x] = 1 If x... View Article

M	T	W	T	F	S	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30	31