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

f(x) must be a linear function. Let f(x)=ax+b. Thenf(ax+b)=6x−ax−bor   a(ax+b)+b=6x−ax−bor   a2=6−a and ab+b=−bi.e.,   a=2 or −3∴  b=0∴  f(x)=2x  or  −3x∴  f(17)=34  or  −51