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
- Aa ^2-b -a=0
- Ba ^2-b -a=1
- Ca ^2+ b - a =-2 ^2
- 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