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AP EAMCET202318 May 2023Morning ShiftMathematicsFunctionsActual

If f : R R and g : R R are defined by f ( x )= x ^3- x and g(x)= 2 x , then the value of x (0,2 ) that satisfy f ( g ( x ))>0 , lie in the interval

Options

  1. A( 2 , )
  2. B(0, 2 ) ( 2 , )
  3. C( 2 , 3 4 ) ( 3 4 , )
  4. D(- 2 , 2 )

Correct answer

C. ( 2 , 3 4 ) ( 3 4 , )

Step-by-step solution

Given : f(x)=x^3-x and g(x)= (2 x) aligned & f(g(x))>0 & f( 2 x)>0 & ^3 2 x- 2 x>0 & ( ^2 2 x-1 ) 2 x>0 & - ^2 2 x 2 x>0 ^2 2 x 2 x < 1 & 2 x < 0 and ^2 2 x 0 & x ( 2 , ) ( 3 2 , 2 ) & 2 x 0 2 x 2 , 3 2 & x 4 , 3 4 & x ( 2 , 3 4 ) ( 3 4 , ) ( 3 2 , 2 ) & Also x ( 2 , 3 4 ) ( 3 4 , ) aligned

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