"tasked with the duty" is correct and usable in written English.
You can use it to describe someone who is assigned a certain task or responsibility. For example, "The manager was tasked with the duty of organizing the charity event."
Engineers tasked with the duty of repairing fatigue-damaged bridges face difficult decisions about the choice of repair method to implement.
Family offices and financial advisors are often tasked with the duty of hosting or mediating a meeting amongst key members of the family to discuss a litany of concerns or to put affairs in order.
His close friends are now tasked with the duty of balancing their grief while not accidentally posthumously outing him to his family.
Speaking of Han Solo, in this version he's tasked with the duty of trying to convince his stepfather, a man named Ovan Marekal, to join the Rebel Alliance -- a man who happens to be the third most powerful man in the galaxy.
Marvin Ellison was appointed CEO of JC Penney in August 2015, and while he still holds the role, he is another key example of a diverse hire tasked with the duty of redirecting a struggling company, and presumed to face harsher criticism if he doesn't succeed.
In March 1943 he was often tasked with the duties of the General der Kampfflieger and in this role he received a preferential promotion to Oberstleutnant (Lieutenant Colonel) on 1 September 1943.
Haydn wrote his Concerto for Fortepiano and Violin in F (Hob.XVIII:6) as a 24-year-old freelance composer tasked with the unhappy duty of writing music to celebrate a would-be lover's taking the veil.
(No one in government, at any level, is tasked with the sworn duty of "defending America," by the way).
Thus, teachers are tasked with the important duty of aiding in the healthy development of students, as well as being required to provide quality intellectual education.
Colonel West was not tasked with that duty.
Unsurprisingly, the two systems tasked with these duties, metabolism and immunity, have evolved to share a common modular architecture that allows extensive bidirectional communication and coordination.
