"fundamental tasks" is correct and usable in written English.
You can use it to refer to tasks or activities which are basic or essential, either to complete a process or for a certain purpose. For example: "Completing the fundamental tasks of gathering and analyzing data was the first step in our project."
Basic fundamental tasks of government have become extraordinarily difficult to enact.
But one of the fundamental tasks of opposition is to oppose – and look at where the failure to do that robustly has got us.
One of its fundamental tasks is to serve as lender of last resort for banks that have trouble raising money on the open market.
Those essential genes carry out the same fundamental tasks that take place in our own cells, like copying DNA and building proteins from genes.
There is something profound and poignant in these struggles, which illustrate one of the fundamental tasks of babyhood: the mastery of the physical environment.
Numerous studies by legal experts of Alabama's capital defense system have documented severe shortcomings, including lawyers who fail to do the most fundamental tasks, like investigating the crime and their clients' backgrounds and presenting closing arguments.
Thousands of Saudis signed a petition in September that demanded the government abolish the guardianship system, which prevents women from engaging in fundamental tasks without the permission of a male relative.
But they share the same fundamental tasks: to reduce skills gaps and shortages, to improve productivity, to boost skills of those working in their sectors and to improve the training that takes place there.
Last November, the G.A.O. said that the commission's books were in such disarray that it had failed at some of the agency's most fundamental tasks: accurately tracking income from fines, filing fees and the return of ill-gotten profits.
But the largely unplanned, spontaneous protests, and the media attention they have commanded, have demonstrated something new: the existence of large numbers of young, educated, urban potential voters who will no longer tolerate a largely unaccountable, unresponsive political elite and bureaucracy incapable of performing the most fundamental tasks.
These collections and archives are fuelled by the lessons of the 70s - that art and politics could be the same, that culture was a necessary means of self-expression, that one of the fundamental tasks black artists faced was to explore the identity of their community by representing its everyday story.
