Carbon fixation is the process of conversion in which carbon-dioxide (inorganic carbon) converts into organic compounds with the help of living organisms and example of this process is photosynthesis.
From the definition, it is confirmed that there is no formation of carbon dioxide takes place i.e. carbon doesn't joined with oxygen molecules.
Thus, carbon fixation is the process in which carbon atoms are added to the molecules of hydrogen and oxygen to make carbohydrates.