The formula C = (5/9) (F −32), where F ≥ −459.67 expresses the temperature “C” in degrees Celsius as a function of the temperature on the \F" scale, in Fahrenheit. Find a formula for the function inverse and interpret it. What is the domain of this inverse function?

1. Start with the given formula:

C = \frac{5}{9} (F - 32)

2. Multiply both sides by 9 to clear the fraction:

9C = 5(F - 32)

3. Divide both sides by 5 to isolate F - 32:

\frac{9C}{5} = F - 32

4. Add 32 to both sides to solve for F:

F = \frac{9C}{5} + 32

So, the inverse function is:

F = \frac{9C}{5} + 32

The domain of this inverse function, corresponding to the range of the original function, is:

C \geq \frac{5}{9}(-459.67 - 32)

Calculating this,

C \geq \frac{5}{9}(-491.67) \approx -273.15

Therefore, the domain of the inverse function is:

C \geq -273.15