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If F 2 3 0 1 Is Defined By F X X X Then F 1 X Is Equal To

Solution: (4) f : (2, 3) → (0,1) f (x) = x - [x] (increasing graph from (0, 1)) limx→2+ f (x) > 0 limx→3- f (x) = 1 f-1(0) = 2 f-1(1)... View Article

If F X Ax X 1 X 1 For What Value Of A Is F F X X

Solution: (5) f (f (x)) = a2x / [ax + x + 1] As, f (f (x)) = x, a2x / [ax + x + 1] = x a2x = (a + 1)x2 + x (a + 1) x2 + (1 - a2) x = 0 (a... View Article

The Function F Satisfies The Functional Equation 3 F X 2 F X 59 X 1 10x 30 For All Real X 1 Then Value Of F 7 Is

Solution: (2) 3 f (x) + 2 f [[x + 59] / (x - 1)] = 10x + 30 x = 7, 3 f (7) + 2 f [11] = 100 --- (1) x = 11, 3 f (11) + 2 f [7] = 140 ---... View Article

If X And Y Are Two Non Empty Sets Where F X Y Is Function Is Defined Such That F C F X X Belongs To C For C Subset X And F 1 D X F X D For D Subset Y For Any A X And B Y Then

Solution: (3) f : X → Y f-1 : Y → X A ⊆ Y and B ⊆ Y f (f-1 (B)) = B... View Article

The Second Degree Polynomial F X Satisfying F 0 0 F 1 1 F X 0 For All X Belongs To 0 1 Is

Solution: (3) f (x) = ax2 + bx + c f (0) = a (0)2 + b (0) + c c = 0 f (1) = a (1)2 + b (1) + c = a + b = 1 f’ (x) > 0 2a + b > 0... View Article

If F R R Is Defined By Then The Correct Matching Of List I From List Ii Is

If f : R → R is defined by . Then the correct matching of List I from List II is List I List II A. f (-5) + f (-4) 1.... View Article

Which Of The Following Functions Is Inverse Of Itself

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

If Y F X X 2 X 1 Then

Solution: (1) & (4) y = f (x) = [x + 2] / [x - 1] f (y) = [y + 2] / [y - 1] yx - y = x + 2 yx - x = 2 + y x = [2 + y] / [y - 1] = f... View Article

If F X X X 1 X 1 Then Fofo Of X Is Equal To

Solution: (1) f (x) = [x] / [x - 1] (fof) (x) = [x / (x - 1)] / [x / (x - 1)] - 1 = x fofof(x) = x / [x - 1]... View Article

If F X 2x 1 X 5 X 5 Then F 1 X

Solution: (2) f (x) = [2x - 1] / [x + 5] = y xy + 5y = 2x - 1 xy - 2x = - 1 - 5y x = [- 1 - 5y] / [y - 2] y = [- 1 - 5x] / [x - 2] = [5x... View Article

If F X Cos Log X Then F X F Y 1 2 F X Y F Xy Has The Value

Solution: (4) cos (log (x)) cos (log (y)) - (1 / 2) [cos (log (x / y)) + cos (log (xy))] = cos (log (x)) cos (log (y)) - (1 / 2) [cos (log... View Article

If X Denotes The Greatest Integer X Then 2 3 2 3 1 99 2 3 2 99 2 3 98 99

Solution: (3) [(2 / 3) + (r / 99)] = {1, r ≥ 33 and 0 (2 / 3) + (1 / 3) = [1] = 1 (2 / 3) + (n / 3) = 2 2 + n = 6 n = 4 = 0 + ∑r=3398 [(2... View Article

If F X A X N 1 N Where A 0 And N Belongs To N Then Fof X Is Equal To

Solution: (2) f (x) = (a - xn)1/n fof(x) = (a - (a - xn)1/n)n)1/n = (a - a + xn)1/n = x... View Article

If F 0 1 F 1 5 And F 2 11 Then The Equation Of Polynomial Of Degree Two Is

Solution: (2) Given: f (0) = 1, f (1) = 5 and f (2) = 11 f (x) = ax2 + bx + c f (0) = 1 f (0) = c = 1 c = 1 f (2) = 11 4a + 2b + 1 = 11... View Article

If G X 1 X X And F G X Is Equal To

If g(x) = 1 + x - [x] and f (g (x)) is equal to 1) x 2) 1 3) f(x) 4) g(x) Solution: (2) g(x) = 1 + x - [x] fog (x) = f [g(x)] = f [1 +... View Article

If F R R Is Given By Then Fof Root 5

If f : R → R is given by . Then, (fof) (√5) = 1) 1 2) -1 3) √3 4) 0 Solution: (1) Let x = √5, (fof) (√5) = f (f (√5)) = f (0) = 1... View Article

If F R R And G R R Are Defined By F X X X And G X X For X Belongs To R Where X Is The Greatest Integer Not Exceeding X Then For Every X Belongs To R F G X Is Equal To

Solution: (2) f (x) = x -[x] = {x} --- (1) g(x) = [x] f (g(x)) = f ([x]) = 0... View Article

If Q Denotes The Set Of All Rational Numbers And F P Q Root P 2 Root Q 2 For Any P Q Belongs To Q Then Observe The Following Statements

Solution: (4) f (p/q) = √p2 - √q2 (p / q ϵ Q) f (p / q) ϵ R, (p / q ϵ Q) √p2 - √q2 ϵ R, (p / q ϵ Q), p / q = 4 / 5 √16 - 25 = √-9 = 3i ∉ R,... View Article

If F X Ax B G X Cx D Then F G X G F X Is Equivalent To

Solution: (3) f (x) = ax + b g (x) = cx + d f{g(x)} = a (cx + d) + b = acx + ad + b g {f(x)} = c (ax + b) + d = acx + bc + d f{g(x)} = g... View Article

If F X F 1 X F X F 1 X And F 3 28 Then F 4 Is Equal To

Solution: (1) f (x) • f (1 / x) = f (x) + f (1 / x) f (x) [f (1 / x) - 1] = f (1 / x) f (x) = f (1 / x) / [f (1 / x) - 1] --- (1) When x =... View Article

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