Is the following function a secure PRG?
Given $F$ is a secure PRG and $k$ is choosen random from key space $K$.
$$G(x) = F(k,x) \oplus F(k,x \oplus 1^s)$$
My solution is $x \oplus 1^s = x'$ so $G(x)$ becomes $f \oplus f'$ with $f = F(k,x)$ and $f' = F(k,x')$. Clearly $f$ and $f'$ are PRG, i.e. generate random strings; and $\oplus$ of these will be random.
Correct me if I am wrong.