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)=

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

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.