When looking at either The Codex or Code Reference there’s usually a little snippet at the bottom which says:
Since: WordPress x.x.x
If we take a look at wp_enqueue_script() for example we see toward the bottom above the contributor notes that it has been around:
Since: WordPress 2.1.0
Now we can use the WordPress Release Chart to find out when 2.1.0 came out, which it did so January 22, 2007. So this function has been around for roughly ~9 years.