Multitask works as both an adjective and a verb. Its adjectival sense is the original, arising in the early 1960s to describe computing systems in which multiple processes execute simultaneously. The verb sense—to perform multiple tasks at once—came about soon thereafter, as did the participial noun multitasking. Each of these terms remained primarily in the computing sphere before first gaining broader use in the late ’80s and early ’90s.
Multitask doesn’t require a hyphen, but the hyphenated form appears often and is not a misspelling. There are no clear rules governing whether to use hyphens when forming words with living prefixes like multi-, and many people fall back on hyphenation when they’re unsure whether a compound word is dictionary-approved. So both multitask and multi-task are acceptable spellings, but there’s no reason to use the two-word, unhyphenated multi task. The word falls apart if its two main parts don’t work as one.
Multitask control will enable you to get many jobs on the system at one time, even unrelated jobs. [Information Display (1962)]
For example, a PL/I program involving multitasking would have a separate virtual processor for each task, but all their segments would be shared. [Software engineering (1970)]
Ameden believes this may be the first time anyone has multitasked an Apple computer this way. [InfoWorld (1981)]
Multitask models, on the other hand, are those that treat a variety of such tasks within a single unifying framework. [Quantitative Modeling of Human Performance in Complex, Dynamic systems (1990)]
Children like Diane have no way of knowing they can multitask successfully, so they do not even try to develop this skill.[Dreamers, Discoverers & Dynamos (1990)]
Ono has never been a multitasker; she enjoys and demands complete focus. [Telegraph (2012)]