# Function can be tricky

Algebra Level 3

Let $$f(x)$$ be a function with non-negative integer coefficient(s) but with power(s) of $$x$$ not necessary integer(s) such that:

$$\begin{cases} f(0) & =2046 \\ f(1) & =2047 \\ f(2048) & =2048 \end{cases}$$

Find $$f(177147)$$.

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