JEE Main20249 Apr 2024Evening ShiftMathematicsFunctionsActual

For a differentiable function f: R R , suppose f^ (x)=3 f(x)+ , where R , f(0)=1 and _ x - f(x)=7 . Then 9 f (- _ e 3 ) is equal to_________

Correct answer

Step-by-step solution

aligned & d y d x -3 y= & If =e^ -3 d x =e^ -3 x & y-e^ -3 x = e^ -3 x d x & y e^ -3 x = e^ -3 x -3 +c & (* e^ 3 x ) & y= -3 +C e^ 3 x aligned on substituting x =0, y =1x - , y=7 we get y=7-6 e^ 3 x 9 f (- _e 3 )=61

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