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AP EAMCET2003MathematicsFunctions

If e^ f(x) = 10+x 10-x , x (-10,10) and f(x)=k f ( 200 x 100+x^2 ) , then k is equal to

Options

  1. A0.5
  2. B0.6
  3. C0.7
  4. D0.8

Correct answer

A. 0.5

Step-by-step solution

We have, e^ f(x) = 10+x 10-x f(x)= 10+x 10-x Given that f(x)=k f ( 200 x 100+x^2 ) 10+x 10-x =k 10+ 200 x 100+x^2 10- 200 x 100+x^2 =k 1000+10 x^2+200 x 1000+10 x^2-200 x =k x^2+100+20 x x^2+100-20 x =k (x+10)^2 (10-x)^2 =2 k 10+x 10-x 10+x 10-x =2 k 10+x 10-x 2 k=1 k= 1 2 =0.5

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