John Hume walks among his rhinos — he’s the custodian of more than 1,500 of the animals — at his private Buffalo Dream Ranch in South Africa. (Trophy LLC/The Orchard)

The documentary “Trophy” takes a multifaceted approach to big-game hunting, a contentious issue that many, on both sides of the debate, consider quite clear cut. It does so by posing a question that may challenge assumptions: Can the commercial exploitation of animals help — rather than harm — threatened species?

Co-directed by Shaul Schwarz and Christina Clusiau, the movie largely focuses on two superficially similar yet contrasting figures. When we meet Phillip Glass, a Texas hunter and sheep farmer, it is through a quintessentially all-American scene, as he takes his young son out on his first buck hunt. When we are introduced to South African rancher John Hume, he is leading an expedition to tranquilize a rhinoceros, and then saw off its horn.

These scenes, while perhaps sensationalistic, set up the film’s central quandary: Both men say they love animals, but their actions — and their feelings — seem in conflict with their words. “I love those lambs,” Glass says, of his livestock, “even the ones that are going to be somebody’s lamb chop this summer for July Fourth. But that’s what they’re for.”

Hume’s position may be more immediately sympathetic. By cutting off the horns of the rhinos he raises, he is trying to make the animals less attractive to poachers. A conservationist, Hume explains that the number of rhinos killed by poachers has skyrocketed, despite a South African ban on the sale of their horns, which some believe to have magical properties. Legalizing the sale of rhino horn, including those that he harvests non-lethally, could be the only way to save the animals from extinction, by financing Hume’s operation — in essence, a sanctioned form of animal exploitation.

Statistics seem to favor Hume’s argument. On the other side of the debate, the lion population has increased over the past century, in part because of ranches that breed the big cats in captivity — not as a sanctuary, but as a farm, producing game for hunters to kill. One rancher sums up his mixed feelings: “When you see [animals] and feed them every day,” he says, on the verge of tears, “you get attached. But there comes a day when you have to let go.” There’s another paradox: More lions mean more attacks on nearby villagers’ livestock — and sometimes on villagers themselves.

At first, the film seems to vilify hunting, as Shaul and Clusiau take us to the Safari Club convention, a Las Vegas showcase for wealthy hunters willing to shell out tens and even hundreds of thousands of dollars for the opportunity to go after what are known as the “big five”: buffaloes, leopards, lions, elephants and rhinos. (Bagging a rhino in its native habitat will set you back $350,000.)

Footage of hunters laughing as they pose for photos with their kill will probably strike many viewers as horrifying. But, as the filmmakers make clear, there can be reasons to hunt, apart from sport. In addition to controlling such dangerous predators, the meat from a single elephant can feed an entire village — one whose population might have otherwise gone hungry.

Late in the film, the directors take us to a rally protesting the killing of Cecil, a beloved, (and nearly tame) lion that had been an attraction at a park in Zimbabwe, and whose 2015 death became a rallying cry for anti-hunting activists worldwide. “We will shame these people,” one protester says, unwilling to entertain that there might be another side to the emotionally fraught story.

To its credit, “Trophy” neither shames its subjects nor offers an easy solution. Rather, it takes a reasoned and thought-provoking view — from many angles — of a problem for which there is, as “Trophy” argues, no quick or simple fix.

Unrated. At the AFI Silver Theatre. Contains strong language and graphic footage of animal killings. 108 minutes.