If `f: R^+vecR^+` is a polynomial function satisfying the functional equation `f(f(x))=6x=f(x),t h e nf(17)` is equal to 17 (b) `51` (c) `34` (d) `-34`

Options

A. 17
B. -51
C. 34
D. -34

Answer

B, C

Explanation

`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`