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If f: R^+rightarrowR^+ is a polynomial f...

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

A

17

B

51

C

34

D

-34

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)` must be a linear function. Let `f(x)=ax+b.` Then
`f(ax+b)=6x-ax-b`
`or a(ax+b)+b=6x-ax-b`
`or a^(2)=6-a and ab +b= -b`
I.e., ` a=2 or -3`
` :. b=0`
` :. f(x) =2x or -3x`
` :. f(17)=34 or -51`
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