Let $G$ $PRG$ and $G'(s)$ equal to the first $n$-bits of $G(s)$, where $|s| = n$. Show that $F_k(x) = G'(k) ⊕ x$ is not a $PRF$.
Lets assume a $k$ and 2 messages $x_1$ and $x_2$. So, for $x_1$ I have $F_k(x_1) = G'(k) ⊕ x_1$, for $x_2$ we have $F_k(x_2) = G'(k) ⊕ x_2$. If the attacker does $F_k(x_1) ⊕ F_k(x_2)$ he gets $x_1 ⊕ x_2$. And then he can simply $XOR$ that by $x_1$ or $x_2$ and then get the message from that.
I have no idea if this is the correct way to prove this. Can you give my any hint if this is the correct way to show that a function is not $PRF$, maybe I have to do a proof by contradiction ?
I also know that a $PRG$ must not be predictable, if it is then that's not good, so for the function $F$ to use $G'$ as the $PRG$ which is always the first $n$-bits of $G$ it's not good because it violates the pseudorandomness property. I don't know if this is correct or helpful at all.