He resolved to look into the old man's background.

If the cops went so far as to look into his background, they wouldn't find anything.

But if he did look further into her background, she couldn't afford to wait and discover it after the fact.

But he said his workers, and other human rights groups, had looked into his background.

I think we need to look into your background in a bit more depth.

What reason would he have for looking that far into my background?

"Look into her background, see if there's something odd there."

There's no law against my looking into someone's background, provided we're dealing with public record.

I've been looking into her background, in a manner of speaking.

There are a lot of reasons why someone doesn't check out right off quick when you begin to look into her background.