Question

Scientists have found a relationship between the temperature and the height above a distant planet's surface. T(h), given below, is the temperature in Celsius at a height h kilometers above the planet's surface. The relationship is as follows:

T(h) = 41-1.25h

Let T⁻¹ be the inverse function of T. Take x to be the output of the function T⁻¹(x).

Explain the meaning of T⁻¹(x)

Answer 1

T⁻¹(x) is the inverse function of T(h), reversing the original relationship to find the height at which a specific temperature x occurs on a distant planet. Using temperature in Celsius at a height h kilometers.

Step-by-step explanation:

Scientists have found a relationship between the temperature and the height above a distant planet's surface, represented by the function T(h) = 41 - 1.25h, which gives the temperature in Celsius at a height h kilometers above the planet's surface.

The inverse function, T⁻¹(x), essentially reverses this process. If T(h) tells us the temperature at a given height, T⁻¹(x) tells us the height at which a certain temperature x is observed. For example, if we want to find the height where the temperature is 20°C, we would calculate T⁻¹(20).

To obtain T⁻¹(x), one would rearrange the original function to solve for h in terms of x, hence finding the height corresponding to the given temperature. This inverse function is useful in scenarios where knowing the altitude at which specific temperature conditions occur is important for scientific exploration and research.