Q.

If function f satisfies the relation fx×f'-x=f-x×f'x for all x, and f(0) = 3, and if  f(3) =3, then the value of f(-3) is ____

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answer is 3.

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Detailed Solution

fx.f'-x=f-x.f'xor    f'x×f-x-fx×f'-x=0or   ddxfxf-x=0or    fxf-x=kGiven  f02=k=9    or   k=9Then  f3f-3=9    or   f-3=3
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