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MHT CET202311 May 2023Morning ShiftMathematicsFunctionsActual

Let f (x)= ( x), 0 < x < and g (x)= ⁻¹ ( e ^ -x ), x 0 . If is a positive real number such that a=(f g)^ ( ) and b=(f g)( ) , then

Options

  1. Aa ^2-b -a=0
  2. Ba ^2-b -a=1
  3. Ca ^2+ b - a =-2 ^2
  4. Da ^2+b +a=0

Correct answer

B. a ^2-b -a=1

Step-by-step solution

array ll & f (x)= ( x), 0 < x < and & g (x)= ⁻¹ ( e ^ -x ), x 0 & ( fog) (x)= [ ( ⁻¹ e ^ -x ) ]= ( e ^ -x )=-x . & ( fog )^ (x)=-1 & a =( fog )^ ( )=-1 and b =( fog )( )=- & These values satisfy only option (B). & Option (B) is correct. array

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