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\paragraph{Problem 6 (20 points)}
Let $F:= \{ f^n: \{0, 1\}^n \rightarrow \{0, 1\}^{n} \}_{n\in\mathbb{N}}$ be a family of one-way functions.
Let $G:= \{ g^n: \{0, 1\}^n \rightarrow \{0, 1\}^{n-1} \}_{n\in\mathbb{N}}$ be a family of functions such that $g^n(x)$ outputs the first $n-1$ bits of $f^n(x)$.
Show that there exists a family of one-way functions $F$ such that $G$ is NOT a family of one-way functions.
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