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AP EAMCET202021 Sep 2020Morning ShiftMathematicsFunctionsActual

If (2 f( x)+f( x)=x ), then (f^ (x)= )

Options

  1. A( 1 1-x^2 )
  2. B( -1 1-x^2 )
  3. C( x 1-x^2 )
  4. D( -x 1-x^2 )

Correct answer

A. ( 1 1-x^2 )

Step-by-step solution

It is given that, (2 f( x)+f( x)=x ) ...(i) by replacing (x ) by ( 2 -x ), we get (2 f( x)+f( x)= 2 -x ) ...(ii) from Eqs. (i) and (ii), we get (3 f( x)=3 x- 2 ) ( 3 f(x)=3 ⁻¹ x- 2 ( . ) on replacing (x ) by ( . ⁻¹ x ) ) Now, on differentiating both sides w.r.t. ' (x ) ', we get (3 f^ (x)=3 1 1-x^2 f^ (x)= 1 1-x^2 ) Hence, option (a) is correct.

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