I am struggling with a property of combined hash function and more precisely concatenation. I have seen that concatenating two collision resistant hash functions preserves this property (same for 2nd preimage resistance). But not always for the first preimage. Indeed, some explains that if the two concatenated hash functions are dependent, the result function could be first preimage weak even if the concatenated functions are preimage resistant. I don't see how it could happen.
First image resistance: From y=H(x), it is computationally infeasible to find any input which hashes to that output y.