Yes, but the Avalanche effect does not mean it is not invertible. It is possible to design a one way hash function with remarkable avalanche (50% of flipped bit

Yes, but the Avalanche effect does not mean it is not invertible. It is possible to design a one way hash function with remarkable avalanche (50% of flipped bits on average after 1 bit change in input) effect but that is easily invertible. The simplest would be an hash function that outputs an N-bit hash where M bits are a pseudo-random sequence of bits (depending on the input, let's say SHA1(input)) that are used to key a stream cipher, and the rest N-M bits are the XOR between the stream cipher output and part of the input of the hash function. Perfect Avalanche effect, but the function is invertible.