A mutagen can be defined as the agent which can be physical or chemical that changes DNA of an organism in such a way that the frequency of mutation increases.
This does not means that all the mutations are caused by mutagens. There are many more reasons for the mutation to take place in the body.
The mutagens can be any physical or chemical agent which can affect the DNA. The x-rays, UV rays and some chemicals are mutagens that increases the chances of mutation in body.
The answer is through facilitated diffusion. It is then called as the transport of substances in a biological membrane from a higher concentration to a lower concentration area though carrier proteins. Hope this is the right answer and would be of help.