1. **State the problem:** Find the inverse of the relation given by the set of ordered pairs $\{(-3,-7), (0,-1), (5,9), (7,13)\}$ and determine if the inverse is a function. 2. **Recall the definition of inverse relation:** The inverse of a relation swaps each ordered pair's components. If the original relation has pairs $(x,y)$, the inverse has pairs $(y,x)$. 3. **Find the inverse:** Swap each pair: $$\{(-7,-3), (-1,0), (9,5), (13,7)\}$$ 4. **Determine if the inverse is a function:** A relation is a function if each input (first element) corresponds to exactly one output (second element). 5. **Check the inverse pairs:** The first elements are $-7, -1, 9, 13$, all distinct. 6. **Conclusion:** Since all first elements in the inverse are unique, the inverse relation is a function. **Final answer:** Inverse relation: $$\{(-7,-3), (-1,0), (9,5), (13,7)\}$$ The inverse is a function because each input maps to exactly one output.