Question

Scientists have found a relationship between the temperature and the height above a distant planet's surface. , given below, is the temperature in Celsius at a height of kilometers above the planet's surface. The relationship is as follows.
T(h)= 30.5- 2.5h

Complete the following statements.

Let T ^-1 be the inverse function of T. Take x to be an output of the function T.
1. Which statement best describes T^-1 (x)?

a. The reciprocal of the temperature (in degrees Celsius) at a height of x kilometers.
b. The height above the surface (in kilometers) when the temperature is x degrees Celsius.
c.The temperature (in degrees Celsius) at a height of x kilometers.
d. The ratio of the temperature (in degrees Celsius) to the number of kilometers, x.

2. T^-1(x)=_______
3. T^-1 (15)=______

Answer 1

Answer:

1) Option B is correct.

The inverse of the function, T⁻¹(x), represents the The height above the surface (in kilometers) when the temperature is x degrees Celsius.

2) T⁻¹(x) = 12.2 - 0.4x

3) T⁻¹(15) = 6.2 m

Step-by-step explanation:

1) The inverse of a function is a function that reverses the effects of the original function on the variable that determines the original function's value.

T(h) = 30.5 - 2.5h

The original function takes the height in kilometres and converts it to temperature at that point in degree Celsius, So, the inverse function will take the temperature in degree Celsius and produce the corresponding height in kilometres.

So, it is the The height above the surface (in kilometers) when the temperature is x degrees Celsius.

The inverse functuon is given as T⁻¹ (x)

2) To obtain T⁻¹(x)

T(h) = 30.5 - 2.5h

We make h the subject of formula

2.5h = 30.5 - T

h = (30.5 - T)/2.5

h = 12.2 - 0.4T

T⁻¹(x) = 12.2 - 0.4x

3) T⁻¹(x) = 12.2 - 0.4x

when x = 15°C

T⁻¹(15) = 12.2 - 0.4(15) = 6.2 m