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If F R R Is Defined By F X 2x 3 Then F 1 X

Solution: (1) f (x) = 2x + 3 y = 2x + 3 y - 3 = 2x x = [y - 3] / 2 f -1 (x) = [x - 3] / 2... View Article

If F X X 2 2bx 2c 2 And G X X 2 2cx B 2 Are Such That Min F X Max G X Then Relation Between B And C Is

Solution: (4) f (x) = x2 + 2bx + 2c2 = (x + b)2 + 2c2 - b2 Minimum of f (x) = 2c2 - b2 g (x) = - x2 - 2cx + b2 Maximum of g (x) =... View Article

If F 1 1 R Be Such That F Cos 4 Theta 2 2 Sec 2 Theta For Theta Belongs To 0 Pi 4 Pi 4 Pi 2 Then Values Of F 1 3 Is Are

Solution: (1) and (2) F : (-1, 1) → R θ ∈ (0, π / 4) ⋃ (π / 4, π / 2) cos 4θ = 1 / 3 cos 2θ = ± √(1 - cos 2θ) / 2 = ± √[1 + (1 / 3)] / 2 =... View Article

If F X X 2 2 2 X 2 Then F 1 X Is Equal To

Solution: (3) f (x) = (x + 2)2 - 2 y = (x + 2)2 - 2 y + 2 = (x + 2)2 x = √y + 2 - 2 f-1 (x) = √(x + 2) - 2... View Article

If The Function F X A X A X 2 Where A 2 Then F X Y F X Y Is Equal To

Solution: (3) f (x) = [ax + a-x] / 2 f (x + y) = [ax+y + a-(x+y)] / 2, f (x - y) = [ax-y + a-(x-y)] / 2 f (x + y) + f (x - y) = (1 / 2)... View Article

If F X 1 X X 2 1 X 2 Then F X Will Be

Solution: (2) f (x + [1 / x]) = x2 + (1 / x2) Let (x + [1 / x]) = t (x2 + [1 / x2]) + 2 = t2 (x2 + [1 / x2]) = t2 - 2 f (t) = t2 - 2 f... View Article

If R Is The Set Of All Real Numbers And F R R Is Given By F X 3x 2 1 Then The Set F 1 1 6 Is

Solution: (2) f (x) = 3x2 + 1 y = 3x2 + 1 f -1 (x) = √(x - 1) / 3 For 1 ≤ x ≤ 6 -√5 / 3 ≤ f -1 (x) ≤ √5 / 3 Range of f -1 (x) is [-√5 /... View Article

If F X X 2 3x 1 Then F F X Is Equal To

Solution: (1) f (x) = (x + 2) / (3x - 1) f {f (x)} = f ((x + 2) / (3x - 1)) = {[x + 2] / [3x - 1]} + 2 / 3 {[x + 2] / [3x - 1]} -1 = 7x / 7 = x... View Article

If F X Root X And G X 2x 3 Then Domain Of Fog X Is

Solution: (5) (fog) (x) = f (g (x)) = √g (x) f (g (x)) = √2x - 3 2x - 3 ≥ 0 2x ≥ 3 x ≥ 3 / 2 x ∈ [3 / 2, ∞)... View Article

Let F X X 1 2 For X 1 If G X Is A Function Whose Graph Is The Reflection Of The Graph Of F X In The Line Y X Then G X Is Equal To

Solution: (4) f (x) = (x + 1)2 for x ≥ -1 g(x) = reflection of f(x) in the line y = x f (x) = (x + 1)2 y = (x + 1)2 (x + 1) = ± y x =... View Article

If F K X 1 K Sin K X Cos K X Where X Belongs To R And K 1 Then F 4 X F 6 X Is Equal To

Solution: (4) fk(x) = 1 / k (sink x + cosk x) f4 (x) - f6 (x) = 1 / 4 (sin4 x + cos4 x) - 1 / 6 (sin6 x + cos6 x) = 1 / 4 [1 - 2 sin2 x cos2... View Article

The Range Of The Function F X X 2 6x 7 Is

Solution: (2) f (x) = x2 - 6x + 7 f ‘ (x) = 2x - 6 f ‘ (x) = 0 ⇒ x = 3 f ‘’ (x) = 2 > 0 f (3) = 32 - 6 * 3 + 7 = 9 - 18 + 7 = -2... View Article

The Domain Of The Function F X Ln X X Is

Solution: (1) f (x) = ln (x - [x]) = ln {x} {x} ≠ 0 {x} > 0 Domain: x ∈ R... View Article

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

Solution: (1) f (x) = √(x - 1) (3 - x) = √- x2 + 4x - 3 = √- x2 + 4x - 4 + 1 = √1 - (x - 2)2 The maximum value of f (x) is 1 when (x -... View Article

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

Solution: f (x) = x2 / [x2 + 1] f (x) = y x2 / [x2 + 1] = y x2 = x2y + y x2 = y / [1 - y] x = √y / [1 - y] y / [1 - y] ≥ 0 y / [y - 1]... View Article

If F X 2x 6 3x 4 4x 2 Then F X Is

Solution: (2) f (x) = 2x6 + 3x4 + 4x2 f ‘ (x) = 12x5 + 12x3 + 8x The power is odd in the above expression. Replace x by -x f ‘ (-x) = -... View Article

If F R R Is Defined By F X X X 1 2 For X Belongs To R Where X Is The Greatest Integer Not Exceeding X Then X Belongs To R F X 1 2 Is Equal To

Solution: (3) f (x) = x - [x] - 1 / 2 x = [x] + {x} f (x) = {x} - (1 / 2) f (x) = 1 / 2 {x} = 1 0 ≤ {x} < 1 Not possible f (x) = 1 /... View Article

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