Problem of the Week

Problem 16

Let’s take a $\textit{recursive}$ function $( F(x) = ax + b )$ .

$\textbf{i)}$ Express $( F(F(b)) )$ and $( F(F(F(b))) )$ in terms of $( a )$ and $( b )$ . What pattern do you notice?

$\textbf{ii)}$ Let $( A = F(F(F(\cdots F(b) \cdots))) )$ , express $( A )$ in terms of $( a )$ and $( b )$ .

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