Math CentralQuandaries & Queries


Question from Mel, a student:

If f(1 + 3x) = 1 * x, solve f(f(x))

Hi Mel,

I think the problem here is that the variable name $x$ is used too many times. Let me reword the problem.

Suppose $f$ is a function which has the property that for each real number $s, f(1+3s) = 1 \times s.$ For a real number $x$ find the value of $f(f(x)).$

Start of the solution:

Let $x$ be a real number. Define $s$ by $1+3s = x,$ in other words $s = \large \frac{x - 1}{3}.$ Then

\[f(x) = f(1+3s) = 1\times s = 1 \times \frac{x - 1}{3} = \frac{x - 1}{3}\]

Can you complete the problem from here?


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