A polynomial satisfies f ( x ) f ( 1/ x ) = f ( x ) + f ( 1/ x ) for x  = 0 and f ( 3 ) = − 26 . Find f ( 4 ) .

f ( x ) = 1 ± x n . The datum gives f ( x ) = 1 − x 3 , so f ( 4 ) = − 63 .

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MathematicsFunctionsFunctional EquationHard3 minQB

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A polynomial satisfies $f (x) f (1/ x) = f (x) + f (1/ x)$ for $x \neq = 0$ and $f (3) = - 26$ . Find $f (4)$ .

Answer:

Solution:

$f (x) = 1 \pm x^{n}$ . The datum gives $f (x) = 1 - x^{3}$ , so $f (4) = - 63$ .

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

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