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AP EAMCET202319 May 2023Morning ShiftMathematicsDifferentiationActual

If f(x) is differentiable on R , f(x) f^ (-x)-f(-x) f^ (x)=0 , f(x) f^ (-x)=0, f(0)=3 and f(3)=9 , then (1+f(-3))^3+1=

Options

  1. A2
  2. B9
  3. C28
  4. D0

Correct answer

B. 9

Step-by-step solution

Given, f(x) f^ (-x)-f(-x) f^ (x)=0 f(-x) f^ (x)-f^ (-x) f(x)=0 d d x [f(-x) f(x)]=0 f(-x) f(x)=c where c= Arbitrary constant when x=0 , then f(0) f(0)=c c=9 when x=3 , then aligned & f(-3) f(3)=c f(-3) .(9)=9 & f(-3)=1 aligned Now [1+f(-3)]^3+1=[1+1]^3+1=9

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