NOT A TEACHER
Supposing Felix is the inspector, the question is fine. However, if a teacher gave the question to me at school I would probably have difficultly understanding the word 'job' in that particular context. It could suggest either job as occupation of policeman (in this case), which Felix is being threatened to lose or either, which seems to me more logical, the particular piece of work i.e. finding the man. However, looking back, I am exaggerating it a bit.Could it be a suitable question?
What did the Chief think about Felix and that job?
To make it plain, there are many possibilities, with which inventive students might come. I would perhaps change 'Felix' to 'inspector'.
Tracking back what I wrote, I feel I failed to anwer.