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AP EAMCET2003MathematicsFunctions

If f: R R and g: R R are defined by f(x)=2 x+3 and g(x)=x^2+7 , then the values of x such that g(x)=x^2+7 , then the values of x such that g(f(x))=8 are

Options

  1. A1,2
  2. B-1,2
  3. C-1,-2
  4. D1,-2

Correct answer

C. -1,-2

Step-by-step solution

we have, f(x)=2 x+3, g(x)=x^2+7g(f(x))=g(2 x+3)=(2 x+3)^2+7=8 4 x^2+9+12 x+7=8 4 x^2+12 x+8=0 x^2+3 x+2=0 (x+1)(x+2)=0 x=-1,-2

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