Q$2$: Let f:$\{0,1\}^$n$->\{0,1\}^$m be a one$-$way function and g:$\{0,1\}^$m$->\{0,1\}^$n be also a one$-$way function.

Would F$=$g$$f: $\{0,1\}^$n$->\{0,1\}^$n be a one$-$way function? Here F$($x$)=$g$($f$($x$)).$

Ans. F $=$ g$$f$=$ g$($f$($x$)).$

Also, f $($x$)$ is one way and g $($x$)$ is one way so g$($f$($x$))$ is one way and so F is one way.