Security of $(k, 2k)$-bit generator for small seeds

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Here is the problem I am working on for context.

problem 4

I have $\epsilon \le 1 - 2^{-k}$ and $\epsilon$ approaches 1 as $k \to \infty$ but I'm stuck on part c). The $f$ is secure iff there does not exist a polynomial-time distinguisher but it seems to me that $ran(f)$ would be fairly easy to find for small seeds.