Given fofof=64x-21，find f(x)

Answer 1

let f(x) = ax + b
then
f(f(x)) = a(ax+b) + b
= a^2 x + ab + b

so a^2 = 64 ---> a = ±8
then ab+b=-21
b = -21/(a+1)

if a=8 , b = -21/9 = -7/3
if a = -8, b = -21/-7 = 3

f(x) = 8x - 7/3 OR f(x) = -8x + 3

check:
if f(x) = -8x + 3
f(f(x)) = -8(-8x+3) + 3 = 64x - 21

if f(x) = 8x - 7/3
f(f(x)) = 8(8x - 7/3) - 7/3
= 64x - 56/3 - 7/3
= 64x - 21

both equations are valid.