MHT CET202014 Oct 2020Morning ShiftMathematicsFunctionsActual

If f(x)= 2 x+3 3 x-2 , x 2 3 then f of is

Options

Aan even function
Bnot defined for all x R
Ca constant function
Dan odd function

Correct answer

D. an odd function

Step-by-step solution

We have, f ( x )= 2 x +3 3 x -2 ( fof )( x )= f [ f ( x )]= f ( 2 x +3 3 x -2 )= 2 ( 2 x +3 3 x -2 )+3 3 ( 2 x +3 3 x -2 )-2 = 2(2 x +3)+3(3 x -2) 3(2 x +3)-2(3 x -2) = 4 x +6+9 x -6 6 x +9-6 x +4 = 13 x 13 = x is an odd function

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