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COMEDK2016MathematicsContinuity and Differentiability

If f(x) is a function such that f^ (x)+f(x)=0 and g(x)=[f(x)]²+ [f^ (x) ]² and g(3)+8 , then g(8)=

Options

  1. A8
  2. B3
  3. C0
  4. D5

Correct answer

A. 8

Step-by-step solution

We have, g(x)=[f(x)]²+ [f^ (x) ]² Differentiate the function g(x)g^ (x)=2 f(x) f^ (x)+2 f^ (x) f^ (x) Use chain rule, 2 f^ (x) [f(x)+f^ (x) ]=2 f^ (x)(0)=0 Hence, g(x) is a constant function g(x)=c , constant But, g(3)=8 , so g(x)=8 For all real x . Hence, g(8)=8

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