The formula $C = \frac{5}{9}(F-32),$ where $F \ge -459.67$ expresses the Celsius temperature $C$ as a function of Fahrenheit temperature $F.$

---

1. Find the formula for the inverse function.
Answer: $C^{-1}(F) =$

2. What is the domain of the inverse function $C^{-1}$ ?
Answer (in interval notation):

---