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Let f(x) = px + q, where p and q are real numbers. Find p+q if f(f(f(x))) = 64x - 105 - 63x + 278.

 Jan 17, 2024
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avatar+266 
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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, \(p+q=58\frac{2}{3}\)

 Jan 18, 2024

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