Homepages are by nature are more of a general catch all… This is where your branding and general call to actions will be found. If you are running paid advertising, like Adwords or some other PPC, you really should have a page that addresses each ad group and each specific problem. Your product or service may solve a multitude of problems and you want to address each one individually.
The more specific you can be, the better your conversion will be.
Given Keyword –> Specific Ad related to keyword –> Specific Landing Page that matches keyword and ad –> Specific Solution on landing page that reads as close to possible to what the potential client searched on –> specific call to action that speaks to the problem = Better Conversions Every Time.
If you have one service that solves one problem your homepage can work. If not, the investment to create a specific lead generation funnel for each problem or category will be more than worth it in the long run.