"encounter the question" is correct and can be used in written English.
You can use it when you want to describe a situation where you or someone else faces or comes across a problem or puzzle that needs to be solved. For example, "When studying for the Science test, I encountered the question I couldn't answer."
Because of his youth, Mr. Fischer-Dieskau had been in no position to make his own choices in the 1930s and '40s, so he didn't encounter the questions about Nazi ties that hung over many a prominent German artist after the war.
Mark Burnett, an impresario of reality television, has surely encountered the question before: How do you make viewers believe what they're seeing?
They started showing neighborhood residents where the fruit was — this was before foraging had entered the public consciousness — and frequently encountered the question: "Is this edible?" "We'd be like, 'Yeah, it's a peach tree,' " Matias said.
But it is impossible to look at some of them now, particularly the ones of Alice Liddell, the namesake of Carroll's masterpiece, without encountering the question of Dodgson's motives.
He's been asked about the whole color issue, of course, and encountered the question of whether Skeeter was black (even once entertaining a call from a man writing a dissertation on race in cartoons).
"These women, being the first to enter this new territory, were the first to encounter the whole question of programming," said Paul E. Ceruzzi, a computer historian at the Smithsonian Institution.
A sort of mental paralysis grips many of us on the left, does it not, when we encounter the "immigration" question in conversations about UK politics?
Any initiatives that join together professionals with specific expertise and care providers who encounter the initial questions are valuable in that they allow a quick inquiry and should be used extensively.
It was the students who went to work for private companies who were far more likely to encounter the obvious moral question: Can you truly claim to be doing good when the only reason you're doing it is to make more money?
That the classes and co-curricular experiences we offer prepare our graduates to encounter the many difficult questions presented in our modern age, especially the dignity of the person.
