If f:R+→R+ is a polynomial function satisfying the functional equation f(f(x))=6x−f(x), then f(17) is equal to

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-51

-34

answer is B.

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Detailed Solution

f(x) must be a linear function, let f(x)=ax+b ⇒f(ax+b)=6x−ax−b ⇒a(ax+b)+b=6x−ax−b ⇒a2=6−a and ab+b=−b ⇒a=2 or −3⇒b=0 ⇒f(x)=2x or −3x⇒f(17)=34 or −51

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