MHT CET202013 Oct 2020Morning ShiftMathematicsFunctionsActual

If f: R R , g : R R are two functions defined by f(x)=2 x-3, ~g (x)=x³+5 then ( fog )⁻¹(x)=

Options

A( 2 x+3 2 )^ 1 2
B( x-7 2 )^ 1 3
C( x-7 2 )^ 1 2
D( x+7 2 )^ 1 3

Correct answer

B. ( x-7 2 )^ 1 3

Step-by-step solution

Given f ( x )=2 x -3, ~g ( x )= x ³+5 aligned ( fog )( x ) &= f [ g ( x )]= f ( x ³+5 ) &=2 ( x ³+5 )-3=2 x ³+7 aligned aligned & Let y=2 x³+7 y-7 2 =x³ & ( y-7 2 )^ 1 3 =x f⁻¹(y)= ( y-7 2 )^ 1 3 &(f g)⁻¹(x)= ( x-7 2 )^ 1 3 aligned

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