Step 1 :Given the function defined by the set of ordered pairs \[\{(-3,6),(2,3),(5,9)\}\]
Step 2 :To find the inverse of a function, we switch the x and y coordinates of each ordered pair.
Step 3 :This is because the inverse of a function 'undoes' the operation of the original function.
Step 4 :So, the inverse of the function is \[\{(6,-3),(3,2),(9,5)\}\]
Step 5 :\(\boxed{\{(6,-3),(3,2),(9,5)\}}\) is the final answer.