Didn' say backed by gold.
It is backed by the US Economy, as legal tender for all transactions. It is an IOU, payable in exchange for goods and services. It is backed by the population of the US who willingly accept it. IE. the government.
If nobody accepted it in the US, it would have no value.
Ditto if we the people 'issue' unlimited/infinite numbers of said stuff. Vietnamese currency is of no value as a 'currency' in the US ... unless, of course, one has an exchange where it can be 'traded' for dollars. Otherwise, no value in US.

Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good ...