This exercise comes from Coursera's "Cryptography" course.
Let $F$ be a PRF, is the following $G(x)=F_{0…0}(x)∥F_{0…1}(x)|| ... ||F_{1…1}(x)$ a PRG?
$F$ is a PRF with $n$ bit key, input, and output length. I know the answer is “NO it isn't!”, but I can't understand why.
Is that because on any input $x$, the keys for every $F$ in the concatenation sequence are fixed, which implies that the $F$ functions are not randomly chosen over $2^{-n}$? Could this be a possible answer?