Question about the Proof of "Pseudorandom generators imply one-way functions" in "Foundations of Cryptography"
Let $n\in \mathbb{N}$, and fix $x,y \in \{0,1\}^n$, $f(x,y)=G(x) \in \{0,1\}^{2n}$. By $f$'s definition, $$\forall x,y_1,y_2 \in \{0,1\}^n,\;f(x,y_1)=f(x,y_2).$$
Hence, if we define the function $f'\colon\{0,1\}^n\to \{0,1\}^{2n}$ by $f'(x)=f(x,0^n)$ we get that $\operatorname{Im}(f)=\operatorname{Im}(f')$ and $\lvert\operatorname{Im}(f')\rvert\le \lvert\{0,1\}^n\rvert=2^n$.