A Quintic Polynomial!

Algebra Level 5

Let \(f(x)\) be a quintic polynomial such that if \(n\) is a positive integer consisting of the only digit \(7\) repeated \(k\) times, then \(f(n)\) consists of the only digit \(7\) repeated \(5k+3\) times.

For example: \(f(77) = 7777777777777\).

Then find the value of \(f(1)\) upto three correct places of decimals.

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