For any y R , let ^ -1 (y) (0, ) and ^ -1 (y) (- 2 , 2 ). Then the sum of all the solutions of the equation ^ -1 ( 6y 9 - y^2 ) + ^ -1 ( 9 - y^2 6y ) = 2 3 for 0 < |y| < 3, is equal to

JEE Advanced 2023 Mathematics question

For any , let and . Then the sum of all the solutions of the equation for , is equal to

Answer: (C)

Let . For , and , so (the root is outside). For ,

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Question ID VK-034115