# 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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