The most common and most likely answer to this crossword clue is the 8 letter word X-RAYING
I've seen this crossword clue in The Times
X
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R
A
Y
I
N
G
More clues leading to the result X-RAYING
Buddy explains!

The straight part
We know that "Investigative job" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case investigative job = x-raying.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does X-RAYING mean?
X-RAYING verb- To take a radiograph of; to obtain an image of using X-ray radiation, especially for the purpose of medical diagnostic evaluation.