The IUPAC name for  is

1. 1-Hydroxypentane-1,4-dione

2. 1,4-Dioxopentanol

3. 1-Carboxybutan-3-one

4. 4-Oxopentanoic acid

Hint: Acid group gets higher priority than ketone group
 
In the given molecule, the acid group gets higher priority than ketone. So, while numbering the chain acid group carbon gets the lowest priority than ketone group carbon. The longest carbon chain contains five carbon atoms. Numbering the chain is as follows:
 
For parent chain pent is used, for ketone group, "oxo" is used and for an acid group, "oic" is used as a suffix.
The IUPAC name of the compound is 4-Oxopentanoic acid