للتحقيق غاية واضحة.

Literally, it is something like:

For the investigation, [there is] a clear aim.

Word by word:

• لِلتحقيق = for the investigation / for the inquiry
• غاية = aim, purpose, end
• واضحة = clear

So the Arabic structure is not word-for-word the same as natural English. Arabic is using a prepositional phrase first, then the noun phrase غاية واضحة.

Because Arabic often uses a nominal sentence with no present-tense verb to be.

In English, you need is or has:

• The investigation has a clear aim
• There is a clear aim to the investigation

In Arabic, the idea is understood without adding a present-tense verb:

• لِلتحقيق غاية واضحة

So this is perfectly normal Arabic, not an incomplete sentence.

The prefix لِـ usually means for or to, but in sentences like this it can also help express an idea close to has or there is ... for.

So لِلتحقيق غاية واضحة can be understood as:

• The investigation has a clear aim
• There is a clear aim to the investigation

This is a very common Arabic pattern:

• لِـ + noun
  • another noun phrase

For example:

• للطالب سؤال = The student has a question / There is a question for the student

Because it comes after the preposition لِـ.

Any noun after a preposition in Arabic is normally genitive:

• لِلتحقيقِ

If full case endings are written, the last vowel is kasra:

• لِلتَّحْقِيقِ

So the final -i sound is there because of the preposition.

Because it is made of two parts:

• لِـ = the preposition for
• التحقيق = the investigation

When they join, you get:

• لِ + التحقيق
• written as للتحقيق

So the first ل belongs to the preposition, and the second ل belongs to the definite article الـ.

It is pronounced roughly as:

lit-taḥqīqi

Here is why:

• The noun is التَّحقيق
• ت is a sun letter
• After الـ, the ل of the article is not pronounced before a sun letter
• Instead, the sun letter is doubled

So:

• written: لِلتَّحْقِيقِ
• pronounced: lit-taḥqīqi

The spelling keeps the ل, but the pronunciation assimilates it to the ت.

Because the meaning is a clear aim, not the clear aim.

• غايةٌ = an aim / a purpose
• الغايةُ = the aim / the purpose

Arabic often uses an indefinite noun in this kind of existential or possessive sentence:

• لِلتحقيق غايةٌ واضحةٌ = The investigation has a clear aim

If you made it definite:

• لِلتحقيق الغاية الواضحة that would sound like a different structure, more like a noun phrase than this simple sentence.

Because adjectives normally come after the noun in Arabic.

So:

• غاية واضحة = a clear aim

This is the normal Arabic order:

• noun + adjective

Also, the adjective must agree with the noun in:

• gender
• number
• definiteness
• case

Since غاية is:

• feminine
• singular
• indefinite
• nominative

the adjective is also:

• واضحةٌ

Because غاية is a feminine noun.

Arabic adjectives must agree with the noun they describe, so:

• غاية = feminine singular
• واضحة = feminine singular

If the noun were masculine, you would use واضح instead.

For example:

• هدف واضح = a clear goal
• غاية واضحة = a clear aim

A common analysis is:

• لِلتحقيقِ = a prepositional phrase functioning as a fronted predicate (خبر مقدّم)
• غايةٌ = the delayed subject/topic (مبتدأ مؤخّر)
• واضحةٌ = adjective describing غاية

So the sentence is a nominal sentence whose core meaning is something like:

• For the investigation there is a clear aim

This fronted order is very natural in Arabic.

Arabic often avoids beginning this kind of sentence with an indefinite noun if there is a smoother alternative.

So instead of starting with:

• غايةٌ واضحةٌ...

Arabic naturally begins with the prepositional phrase:

• لِلتحقيقِ غايةٌ واضحةٌ

This makes the sentence sound more idiomatic and clearer as an existential/possessive statement.

التحقيق can mean different but related things depending on context, such as:

• investigation
• inquiry
• examination
• verification

It comes from the root ح-ق-ق, which has to do with truth, confirmation, and making something certain or established.

So the exact English word depends on context, but grammatically the sentence works the same way whichever nuance is intended.

Yes, often you could say:

• للتحقيق هدف واضح

That would also mean something like The investigation has a clear goal.

The difference is mostly nuance:

• غاية can sound a bit more formal, abstract, or literary: aim, purpose, end
• هدف often feels more like goal, target, objective

Both are valid, but غاية gives the sentence a slightly more formal or elevated tone.