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If f x = tan 1 ° x + log e 123 x log e 1234 - tan 1 ° , x > 0 , then the least value of f f x + f f 4 x is

Options

  1. A0
  2. B8
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Given, f x = tan 1 ° x + log e 123 x   log e 1234 - tan 1 ° ,   x > 0 Now, let tan 1 ° = a ,   log e 123 = b and log e 1234 = c So, f x = a x + b c x - a ⇒ f f x = a f x + b c f x - a ⇒ f f x = a a x + b c x - a + b c a x + b c x - a - a ⇒ f f x = a 2 x + a b + b c x - a a c x + b c - a c x - a = a 2 x + b c x b c + a 2 = x ⇒ f f x + f f 4 x = x + 4 x ∵   x > 0 , then least value = x · 4 x = 2

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