Worst case one way function the worst-case one way function is defined as follows
$$\forall A \exists x : pr(A(f(x))\in f^{-1}(f(x)))\neq 1$$
can you give any example of such function?
Worst-case one-way functions exist if and only if P ≠ NP, therefore, if I were you, I would not expect to get a definitive answer to your question any time soon :).

On the other hand, if you are willing to assume that P ≠ NP, then it is not hard to construct such a function (that is actually exactly a half of the proof of the theorem I stated in the previous paragraph).