From what I have read in my searching on this topic, it looks like the main difference between the forms of bezahlen that either use für or don't use für, is what is made as the direct object. (the emphasis?)
- [jemandem] etwas bezahlen -> to pay [somebody] something
- jemanden [für etwas] bezahlen -> to pay somebody [for something]
- jemandem etwas bezahlen -> to pay for (buy) something for somebody
Also note that the somebody in the first and third bullet points are in dative, whereas the somebody in the second bullet point is in accusative.
In the case of "Die Eltern bezahlen den Liter." from a previous skill, it uses the third bullet point usage above (and just leaves out for whom they are buying the liter), and the "Ich bezahle für die Untersuchung." uses the second bullet point usage, and also leaves out who is being payed.
Here's my understanding on when to use which. The third bullet point seems to basically be for buying something tangible, whereas the second bullet point can also be used for something like paying for a service (or still for some object as well). In the example sentences, the Liter is an object that is bought, whereas the Untersuchung is a service that is paid for.
In Australia we would definitely say examination to describe what the doctor does. We would use investigation more in relation to medical tests such as pathology. For example "I went to the doctor about that pain in my chest. His examination didn't show anything but he thinks it needs investigating so he's referred me for some tests. Now I have to pay for more investigations. " We tend to use "check up" more if someone has something specific they are concerned about and want a doctor's opinion on or if they have a regular visit like an annual medical examination to ensure they are healthy but it is also used in referring to a follow up after treatment and for a routine visit for a chronic condition where there is no particular concern but to make sure everything is going as it should.
In the UK we use investigations to describe a collection of examinations and tests where you know something is wrong but don't know the cause.
A lot of the Americans seem to think of malpractice when it comes to investigation but there's no suggestion of that in the UK. We'd use inquiry for that.
It is very different from a checkup which is a routine thing where nothing particular is wrong. Just for monitoring or something.
Investigation, in the US at least, implies a collection of information more than the performance of an experiment. Any experiments to test the chemical nature of something would usually get called lab work, lab tests, or lab results. Investigation is generally not used in the context of determining what a medical problem is.
Not seeing this having been addressed; a couple of things. Second time through the English tree.
Investigations would not be a medical term. Investigation is more of a criminal term. Police 'investigate' doctors 'examine'.
That is not my major concern. If they say investigate at the doctors office in Germany that's fine, I'm not trying to change that. Better we should all learn that here.
My concern is that while it does accept "exam" it does not recognize "exams" which is simply the plural short form of examinations. So just pointing out that it is inconsistent with in the lesson because 'Untersuchung-en' is the plural form 'investigation-s' so the plural short form of examinations is exams.
It does not but it should accept "exams" .