Let f(x) = px+q, where p and q are real numbers. Find p+q if f(f(f(x))) = 8x+21.
+128472 f(f(x)) = p (px + q) + q
f (f(f(x))) = p [ p (px + q) + q ] + q =
p [ p^2x + pq + q ] + q =
p^3x + p^2q + pq + q = 8x + 21
This implies that
p^3x = 8x
p^3 =8
p = 2
And
p^2q + pq + q = 21 ....so....
(2)^2q + 2q + q = 21
4q + 2q + q = 21
7q = 21
q = 3
So
p + q = 2 + 3 = 5
