Question $4.$ Lef $F$ be a secure pseudorandom function defined over $\{0,1{\}}^n.$

Prove or refute: $F_1(k,x)=F(F(k,0^n),x)$ is a secure PRF$.$

Prove or refute: $F_2(k,x)=F(F(k,0^n),x)||F(k,x)$ is a secure PRF$.$

Prove or refute: $F_3(k,x)=F(k,x)||F(k,F(k,x))$ is a secure PRF$.$