In the late ’60s, the last time that America seemed as divided as it is now (back then it was the counterculture vs. the establishment; today it’s reality-based thinking vs. rabbit-hole fantasy), there was a popular technique of rudeness known as “the put-on.” The obnoxious idea was that if you found yourself confronting someone who was clueless, you should coax out their cluelessness even more by saying things you don’t believe: more far-out than you thought — or maybe more far in. As the lively new documentary “Eat That Question: Frank Zappa in His Own Words” makes clear, Frank Zappa was a master of the put-on — but not just because he bamboozled the “squares.” He presented a put-on to the counterculture too. He was a quirky, daring, idiosyncratic, out-of-the-box musician, but he was also a straight arrow in hippie-anarchist clothing. He hated blandness and fakery and selling out, but the way he challenged all those things was as American as apple pie.

It’s easier now than it was then to see Zappa for what he was: not a rebel like Abbie Hoffman but a rebel like Howard Stern in the ’90s, someone who fashioned himself as an outsider because he had such a highly developed b.s. detector. The put-on began with his look: the mop of curly long hair and the signature thick, black T-square of a goatee — as iconic an example of facial-hair-as-performance-art as Salvador Dalí’s handlebar wisp of a mustache. The way that Frank Zappa looked scared a lot of people (in the context of the culture wars of 1968, he appeared to be the embodiment of everything that was out to destroy America), and he played up that threat by dismissing himself as “ugly.”

It’s true that from a distance, he looked like a slightly mad biker crossed with a defrocked medieval priest. But in “Eat That Question,” which is basically a beautifully edited series of interview clips — conducted, over a period of 25 years, on television, in living rooms and recording studios, at airports and concert settings — we get to see Zappa up close, and he was actually quite an appealing-looking fellow, with an elegant tapered jaw and dark puppy-dog eyes that twinkled as he toyed with whoever he was talking to. In conversation, his voice was a powerful instrument, rich and deep and too direct to be sarcastic. If someone were making a biopic about Frank Zappa, the actor who could do him justice — don’t laugh — is Jon Hamm. Zappa had that combination of handsome severity and forceful flippancy.

He came on like an outrageous hippie pariah, but really, he only played one on TV — or, more accurately, in the rock & roll media diorama that was the counterculture’s version of TV. Though it was often assumed that he was an explorer of controlled substances, he actually hated drugs (and frowned on the use of them by his band members). He was a businessman who started his own record company and lived in a suburban home in L.A. with his wife and four kids. His brand was freakishness, but there was a reason that he fooled almost everyone, and that was his ruling passion: All he wanted to do was to play music — his music, his way. And so (biggest put-on of all) he pretended to be a countercultural satirist.

There is some satire, especially on the early records, along with a fair amount of goofy surrealist horseplay. When I was a teenager, listening to songs like “I’m the Slime” or “Sofa No. 2” or “Florentine Pogen” or “Montana” (“I might be movin’ to Montana soon,/Just to raise me up a crop of…dental floss”), I’d often wonder if I was missing some deep hidden meaning in Zappa’s lyrics. They were an honest reflection of his absurdist sense of humor, but mostly they were there because he was working in a basic medium of pop albums that required songs with lyrics.

It was literally everything between the lines that he cared about. “Eat That Question” shows us the side of Zappa who considered himself a classical composer (he says that when he was growing up, his ambition was to be the missing link between Stravinsky and Edgar Varèse). But he’s most truthful about his music when he describes every record he ever made as part of one gigantic composition. And it truly was. You can pluck moments out of it, like his most seductive pop song (“Peaches en Regalia”) or his catchiest polyrhythmic doodle (“Pygmy Twylyte”) or his most virtuoso bauble (“Inca Roads”) or his most haunting rock anthem (“Muffin Man”) or his most awesome groove for adults (the Grammy-winning album “Jazz From Hell”). Yet you could also throw every single one of his songs and compositions into the air and have them all fall into place on random albums and they might sound even more dazzling. He was a bebop classicist who, paradoxically, thought in jingles.

As his acerbic comments over the decades in “Eat That Question” make clear, he was someone who longed for America to be better: more adventurous, less restricted. That’s why in the ’80s, he became a commonsensical spokesman against Tipper Gore’s PMRC. Much of the way that Frank Zappa thought was ahead of his time, and that may be why he’s now being discovered anew. A second documentary about him is in the works, this one by the gifted actor-turned-filmmaker Alex Winter (“Downloaded,” “Deep Web”), which plans to explore more of the psychodrama that powered his rotating band. Zappa could be a bit of a snob, to the point that even though he at times created music that was beautiful, he didn’t seem to trust beauty. He was taken away from us when he was far too young, and part of the sadness of that is that by the time he died, at 52, of prostate cancer (in 1993), it’s clear that he was mellowing into an elder statesman of pop independence. It was an effortless transition, because he was never stuck in the ’60s or ’70s. The only aspect of that era he brought with him, and fashioned into words to live by, was: Do your own thing.