Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Morning ShiftMathematicsLimitsActual

Let f : R + → R + be a function satisfying f x - x = λ (constant), ∀ x ∈ R + and f x f y = f x y + x , ∀ x , y , ∈ R + . Then lim x → 0 f x 1 3 - 1 f x 1 2 - 1 =

Options

  1. A1 3
  2. B0
  3. C2 3
  4. D1

Correct answer

C. 2 3

Step-by-step solution

Given relation is f x   .   f y = f x y + x   . . . . . 1 Interchanging x and y in equation 1 we get, f y   .   f x = f y x + y   . . . . . . . 2 Again replacing x with f x in equation 2 we get f f x · f y = f y · f x + f x   ⇒ f f x · f y = f y x + y + f x     . . . 3 from equation 2 Again interchanging x and y in equation 3 , we have f f y · f x = f y x + x + f y . . . . . . . 4 Now from equation 3   &   4 we get, f x y + y + f x

Practice Limits on Quantrex Academy →

More from Limits

If _ x 0 ( p 2x + 1 - 2x x + x ) = 1 then the value of ' p ' is 2026_ x 2 ( 1 - x x ) is equal to 2026The value of _ x 3 [ 1 x-3 + 9x 27-x^3 ] is: 2026_ x 0 (1 - 2x)(3 + x) x 4x is equal to: 2026If _ x 3 ( x^2 - ax - 3b x - 3 ) = 5 , then a + b = 2026If f(x) = cases x^2 - 1 & if x 2 x + 1 & if x < 2 cases , then _ x 1 f(x) + _ x 2 f(x) = 2026_ x 4 2 2 -( x+ x)^3 1- 2 x = 2025Let [x] denote the greatest integer less than or equal to x . Then _ x 2⁺ ( [x]^3 3 - [ x 3 ]^3 )= 2025 Full Limits list All AP EAMCET PYQs