First preimage resistance check So I have $H: \{0,1\}^* \rightarrow\{0,1\}^n$ a hash function resistant to the second preimage and to collisions. Let there be a function $H' : \{0,1\}^* \rightarrow \{0,1\}^{n+1}$ with the following properties:

$$H'(x) = \{0||x\; \text{if}\; x∈\{0,1\}^n;\quad 1||H(x) \text{ otherwise}\}$$

Is $H'$ preimage resistant $∀ x$ ?

I know that I have to find an $x$ for which this property fails, but I cannot think of one, could you please help me and explain how to demonstrate this?
Preimage resistance is usually defined not for all the inputs, but for all the outputs, since what you are trying to model is the inability to, given any output $y$, obtain an input $x$ such that $H(x) = y$.

I'm not going to solve the problem for you since you may be able to do it by yourself. Just try to think of the patterns in the output and if this can be related to some input.