Like Sqad, i answer with reservations. My experience is empirical, many years of working in rehabilitation with older people, loads of hip replacements and surgically repaired fractures. As well as a worsening of pre existing and maybe unnoticed dementia, the following can also occur
Affected cognitive function due to slow clearance of anaesthesia...less common nowadays using modern drugs and techniques.
Affected cognitive function due to pain relief meds....usually wears off as meds are no longer needed.
Mini stroke as a result of the operation.
Affected cognitive function due to nutrition/ hydration issues. If someone is borderline dehydrated/malnourished then the interruption to normal intake caused by the surgery can cause problems. additionally if the person is is poorly hydrated and/or has low immune function, they may get a urine infection, the risk of this increases if they need to be catheterised. Symptoms of UTI mimic dementia but reverse when the UTI is treated.
This is why older people are often put on a simple drip before or after surgery or if they are admitted to hospital with other problems eg chest infection. Is a fast effective way of balancing blood sugar and body fluid and supporting kidney and bladder function.