Problem $3(0$ Points$).$ Consider the following conjecture: For every length preserving ${?}^2$ one$-$way

function, the function $f^{\text{'}}(x)=f(x)o+x$ is also one$-$way. Refute it$.$

Hint: Consider the function $h(x_1,x_2)$:$=g(x_1)o+x_2.$ If $g()$ is one$-$way, is $h(x_1,x_2)$ one$-$way too?

Why or why not? Can you use $h()$ to come up with a different one$-$way function $($call it $f())$ which

is both length preserving and one$-$way? Finally, can you use $f()$ to refute the conjecture above?