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If F X 1 2 Tan Pix 2 1 X 1 And G X Root 3 4x 4x 2 Then Domain F G Is Given By

Solution: (3) F : x ∈ (-1, 1) g (x) = √3 + 4x - 4x2 Domain of (f + g) = D (F) ⋂ D (G) 3 + 4x - 4x2 ≥ 0 4x2 - 4x - 3 ≤ 0 (2x + 1) (2x -... View Article

The Domain Of The Function F X Log 2x 1 X 1 Is

Solution: (1) f (x) is defined if a] x - 1 > 0 ⇒ x > 1 b] 2x - 1 > 0 ⇒ x > 1 / 2 c] 2x - 1 ≠ 1 ⇒ x ≠ 1 The domain of f (x) is... View Article

If N Is The Natural Number Then The Range Of The Function F N 8 N P N 4 4 N 6 Is

Solution: (3) f (n) = 8 - n Pn - 4 The domain becomes, 8 - n ≥ 0 and n - 4 ≥ 0 8 ≥ n and n ≥ 4 n - 4 ≤ 8 - n 2n ≤ 12 n ≤ 6 If n = 4,... View Article

If F X Is An Even Function And F X Exists Then F E F E Is

Solution: (2) A function is called even when f (-x) = f (x) f (-x) – f (x) = 0 On differentiating at x = e, f ' (e) + f ' (-e) = 0 f '... View Article

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

Solution: (1) f (x) = x2 + {1 / [x2 + 1]} = [x2 + 1] + {1 / [x2 + 1]} - 1 AM ≥ GM [x2 + 1] + {1 / [x2 + 1]} / 2 ≥ 1 [x2 + 1] + {1 / [x2 +... View Article

The Period Of The Function F X Sin 8x Cosx Sin6x Cos3x Cos2x Cosx Sin 3x Sin 4x Is

Solution: (3) f (x) = [sin 8x cosx - sin6x cos 3x] / [cos2x cosx - sin 3x sin 4x] = [sin 9x + sin 7x] - [sin 9x + sin 3x] / [cos 3x + cos x]... View Article

If F R R And G R R Are Defined By F X X And G X X 3 For X Belongs To R Then G F X 8 5 X 8 5 Is

Solution: (3) f (x) = |x| g (x) = [x - 3] g (f (x)) = g (|x|) = [|x| - 3] x is nearly equal to -8 / 5 g (f (-8 / 5)) = [|-8 / 5| - 3] = (8... View Article

The Domain Of Sin 1 Log 3 X 3 Is

Solution: (1) y = sin-1 x, then x lies between -1 and 1. -1 ≤ log3 (x / 3) ≤ 1 (1 / 3) ≤ x / 3 ≤ 31 1 ≤ x ≤ 9... View Article

The Period Of The Function F X Cosec 2 3x Cot 4x Is

Solution: (4) f (x) = cosec23x + cot 4x The period of cosec²x is π and the period of cosec²3x is π / 3. The period of cotx is π and the... View Article

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

Solution: (3) f (x) = -1 / √4 - x2 √4 - x2 > 0 4 - x2 > 0 x2 < 4 x ≤ 2 Domain is (-2, 2).... View Article

If F 2 3 R Is Defined By F X X 3 3 X 2 Then The Range F X Is Contained In The Interval

Solution: f : [2, 3] → R f (x) = x3 + 3x - 2 f (2) = 23 + 3 * 2 - 2 = 8 + 6 - 2 = 12 f (3) = 33 + 3 * 3 - 2 = 27 + 7 = 34 The interval is... View Article

If F X 1 Root Mod X X Then Domain Of F X Is

Solution: (1) f (x) = 1 / √|x| - x |x| - x > 0 x - x > 0 0 > 0 [not possible] - x - x > 0 -2x > 0 x ∈ (-∞, 0)... View Article

The Domain Of Definition Of The Function F X Root 1 Log E 1 X Is

Solution: (2) f (x) = √1 + loge (1 - x) 1 - x > 0 loge (1 - x) ≥ -1 1 - x ≥ e-1 x ≤ 1 - (1 / e) Domain = (-∞, 1 - [1 / e])... View Article

The Domain Of The Function F X Log 2 Log 3 Log 4 X Is

Solution: (2) f (x) = log2 [log3 (log4 x)] Let log4 x = t In log4 x, x > 0 [log3 (log4 x)] = log3 t, t > 0 (log4 x) > 0 x >... View Article

If F Is A Function With Domain 3 5 And G X 3x 4 Then The Domain Of Fog X Is

Solution: (4) g (x) = |3x + 4| fog(x) = f (g(x)) = f (|3x + 4|) The domain is [-3, 5] -3 ≤ |3x + 4| ≤ 5 0 ≤ |3x + 4| ≤ 5 3x + 4 ≤ 5 -5 ≤... View Article

Range Of The Function F X X 1 X 2 Is

Solution: (3) f (x) = [x / (1 + x2)] 1 + x2 ≠ 0 x2 ≠ -1 x ∈ R Domain: x ∈ R 1 + x2 ≥ 1 f (x) = y = [x / (1 + x2)] yx2 - x + y = 0 D ≥... View Article

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

Solution: (2) f (x) = √cos-1 [(1 - |x|) / 2] 0 ≤ cos-1 θ ≤ π -1 ≤ [(1 - |x|) / 2] ≤ 2 -2 ≤ [1 - |x|] ≤ 2 -3 ≤ -|x| ≤ 1 3 ≥ |x| ≥ -1... View Article

The Domain Of Sin 1 Log 2 X 12 Is

Solution: (5) -1 ≤ [log2 (x / 12)] ≤ 1 (1 / 2) ≤ x / 12 ≤ 2 6 ≤ x ≤ 24 x ∈ [6, 24]... View Article

The Function F X Sec Log X Root 1 X 2 Is

Solution: (2) f (x) = sec [log (x + √1 + x2)] f (-x) = sec [log (-x + √1 + (-x2))] = sec (log (-x + √1 + x2)) = sec log [√1 + x2) - x] *... View Article

The Period Of The Function F Theta 4 4 Sin 3 Theta 3 Sin Theta Is

Solution: (1) f (θ) = 4 + 4 sin3 θ - 3sinθ = 4 - (3 sin θ - 4sin3 θ) = 4 - sin 3 θ f (θ + (2π / 3)) = 4 - sin [3 (θ + 2π / 3)] = 4 - sin... View Article

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