Let F : $\{0,1\}^$n $\backslash$times $\{0,1\}^$n $->\{0,1\}^$n be a pseudorandom function. State whether the following keyed functions H are pseudorandom functions. Support your answer with a formal proof or with a formal analysis of an explicit attack.

$($b$)$ The keyed function H : $\{0,1\}^$n $\backslash$times $\{0,1\}^$n$1->\{0,1\}^2$n is defined as:

Hk$($x$)=$ Fk$($x$||0)||$ Fk$(1||$x$)$