Problem
\[ T(h)=45-1.25 h \] Complete the following statements. Let $T^{-1}$ be the inverse function of $T$. Take $x$ to be an output of the function $I$. That is, $x=T(h)$ and $h=T^{-1}(x)$. (a) Which statement best describes $T^{-1}(x)$ ? The height above the surface (in kilometers) when the temperature is $x$ degrees Celsius. The reciprocal of the temperature (in degrees Celsius) at a height of $x$ kilometers. The temperature (in degrees celsius) at a height of $x$ kilometers. The ratio of the temperature (in degrees celsius) to the number of kilometers, $x$. (b) $T^{-1}(x)=\square$ (c) $I^{-1}(29)=\square$ Continue
Solution
Step 1 ：\(T^{-1}(x)\) is the height above the surface (in kilometers) when the temperature is \(x\) degrees Celsius.
Step 2 ：Set \(T(h) = x\) to find \(T^{-1}(x)\), so \(x = 45 - 1.25h\).
Step 3 ：Rearrange the equation to solve for \(h\): \(1.25h = 45 - x\).
Step 4 ：Solve for \(h\) to get \(T^{-1}(x)\): \(h = \frac{45 - x}{1.25}\).
Step 5 ：\(\boxed{T^{-1}(x) = \frac{45 - x}{1.25}}\)
Step 6 ：The function \(I\) is not defined in the problem, so we cannot find \(I^{-1}(29)\).
