Sentence with separable verb and normal verb

Question

Suppose I have a main sentence , and in it, I use a separable verb first and then a normal verb. How does the general word order look like?

If it is just a normal verb and then a separable verb, the normal verb takes second slot and the separable goes to end.

However, in the question statement's case, should the prefix of the separable verb be at end or the normal verb

Example:

English :

I am beginning to understand the question.

Possible German translations:

1. Ich anfange, die Frage zu verstehen
   
2. Ich fange an, die Frage zu verstehen
   
3. Ich fange, die Frage zu verstehen an.

Which is right, and why is the right one right?

Answer 1

The part "die Frage zu verstehen" is called an extended infinitive (erweiterter Infinitiv), and in the sentence it is an object.

In modern German, the order that is almost exclusively used is to place the extended infinitive after the main sentence:

(2) Ich fange an, die Frage zu verstehen.
Ich bin jetzt sicher, die Frage verstanden zu haben.

It is possible to put an infinitive inside the sentence in a more literary, artistic German, but almost only if the infinitive stands alone. It is also possible, if a special emphasis is intended, to place the infinitive at the beginning.

Sie fingen zu laufen an. (instead of the usual "Sie fingen an zu laufen.")
Mit ihren 60 Jahren noch Klavier spielen zu lernen, traute sie sich nicht zu.

With an extended infinitive, like in your case, it sounds very odd and I would not use it.

(3) Ich fange die Frage zu verstehen an

The first variant is clearly incorrect. First person singular of a separated verb is always the separated form: ich fange an, never ich anfange.

(1) Ich anfange, ...

Answer 2

Two options are correct:

2. Ich fange an, die Frage zu verstehen.

3. Ich fange die Frage zu verstehen an.

Here (2) is the much more commen way to phrase it while (3) is possible but makes it sound unnecessarily complicated (there is no comma in this version). If you replace "anfangen" with the inseparable "beginnen" the only remaining way is (2).

Answer 3

Separable verbs behave like combinations of two verbs. For instance, in declarative sentences the finite verb appears in second position and the non-finite verbs and verbal particles (the separable part of separable verbs) go to the end.

Ich gehe jeden Tag shoppen.
Ich kaufe jeden Tag ein.

In subordinate clauses, the finite verb goes to the end.

(Ich habe kein Geld,)
da ich jeden Tag shoppen gehe
da ich jeden Tag einkaufe

However, the example you give isn't about a combination of two verbs like in the examples above. It is important to know that zu-infinitives can form clauses (marked with square brackets in the following examples). These clauses preferably appear "after the end".

Er hat behauptet, [ jeden Tag shoppen zu gehen. ]
Er hat behauptet, [ jeden Tag einzukaufen. ]

The clausal character of zu-infinitives becomes quite clear when you compare them with a dass-clause.

Er hat behauptet, [ dass er jeden Tag shoppen geht. ]
Er hat behauptet, [ dass er jeden Tag einkauft. ]

Subordinate clauses can however be moved around; for instance, they can easily appear in first position.

[ Dass er jeden Tag shoppen geht, ] wusste ich nicht.
[ Jeden Tag einzukaufen, ], halte ich für Zeitverschwendung.

The technical term for "end" is rechte Satzklammer or Verbalkomplex, while the position "after the end" is known as Nachfeld. For further reference, see for instance Feldermodell des deutschen Satzes.