2025-02-05

1. Domain and Range of $T(d)$:

   • Domain: $\{d\in \mathbb{R}|0\le d\le 5000\}$
   • Range: $\{T(d)\in \mathbb{R}|11\le T(d)\le 86\}$

2. Inverse Function:

   • $d(T)=\frac{T-11}{0.015}$

3. Domain and Range of $d(T)$:

   • Domain: $\{T\in \mathbb{R}|11\le T\le 86\}$
   • Range: $\{d\in \mathbb{R}|0\le d\le 5000\}$

4. Meaning of the Inverse Function:

   • The inverse function calculates the depth required to reach a given temperature.

5. Calculation Using the Inverse:

   • $d(22)=\frac{22-11}{0.015}=733\text{m}$
   • At a temperature of $22^{\circ }\text{C}$, the depth is approximately $733\text{m}$.