+1791 Let f(x) = px + q, where p and q are real numbers. Find p+q if f(f(f(x))) = 64x - 105 - 63x + 278.
+266 Im just going to brute force it. You may find other answers.
\(f(f(f(x))) = 64x - 105 - 63x + 278\)
\(f(f(px+q)) = 64x - 105 - 63x + 278\)
\(f(p^2x+pq+q) = 64x - 105 - 63x + 278\)
\(p^3x+p^2q+pq+q = 64x - 105 - 63x + 278\)
From this, we get that
\(p^3 = 64 - 63 = 1\)
\(p = 1\)
Therefore,
\(3q = 173\)
\(q = 57\frac{2}{3}\)
So, \(p+q=58\frac{2}{3}\)
