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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Suppose that f(x) is defined and positive for all real numbers x . If f(x) increases for x 0 and decreases for all x 0 , and g(x)= 1 f ( 1 x ) then

Options

  1. Ag increases for all real x
  2. Bg increases for x < 0
  3. Cg decreases for x > 0
  4. Dg increases for x > 0

Correct answer

C. g decreases for x > 0

Step-by-step solution

f(x) 0 and f^ (x) 0 for x 0f^ (x) 0 for x 0 Now g(x)= 1 f ( 1 x ) g^ (x)= -1 f^2 ( 1 x ) f^ ( 1 x ) ( -1 x^2 ) So for x 0 g^ (x) 0x 0 g^ (x) 0

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