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 Celsiusat a height ofh kilometers above the planet's surface. The relationship is as follows.T (h) 30.5-2.5hComplete the following statements.- 1Let Tbe the inverse function of TTake x to be an output of the function T?(a) Which statement best describes T(x)?XThe reciprocal of the temperature (in degrees Celsius) at a height ofx kilometers.The height above the surface (in kilometers) when the temperatureis x degrees Celsius.The temperature (in degrees Celsius) at a height of x kilometers.The ratio of the temperature (in degrees Celsius) to the number ofkilometers, x- 1(x) =(b) Т- 1Т(15)(c)OO

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Asked Oct 27, 2019
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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 ofh kilometers above the planet's surface. The relationship is as follows.
T (h) 30.5-2.5h
Complete the following statements.
- 1
Let T
be the inverse function of T
Take x to be an output of the function T
?
(a) Which statement best describes T(x)?
X
The reciprocal of the temperature (in degrees Celsius) at a height of
x kilometers.
The height above the surface (in kilometers) when the temperature
is x degrees Celsius.
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
- 1
(x) =
(b) Т
- 1
Т
(15)
(c)
OO
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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 ofh kilometers above the planet's surface. The relationship is as follows. T (h) 30.5-2.5h Complete the following statements. - 1 Let T be the inverse function of T Take x to be an output of the function T ? (a) Which statement best describes T(x)? X The reciprocal of the temperature (in degrees Celsius) at a height of x kilometers. The height above the surface (in kilometers) when the temperature is x degrees Celsius. 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 - 1 (x) = (b) Т - 1 Т (15) (c) OO

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Expert Answer

Step 1

The relation between the temperature and the height above a distance planet is,

T(h) 30.5-2.5h
(a)Obtain inverse of T
That is, replace h by T-1 (h) and T(h) by h in the above relation
T(h) 30.5-2.5h
h 30.5 2.5T (h)
2.5T h 30.5 - h
30.5 h
т"():
2.5
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T(h) 30.5-2.5h (a)Obtain inverse of T That is, replace h by T-1 (h) and T(h) by h in the above relation T(h) 30.5-2.5h h 30.5 2.5T (h) 2.5T h 30.5 - h 30.5 h т"(): 2.5

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Step 2

(b) Given that x  is the output for the temperature T .

Obtai...

30.5 h
т" ():
2.5
т (:)-т"(т(h)
=h
Answer: The reciprocal ofthe temperature (in degree Celsius) at a height ofx
kilometers
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30.5 h т" (): 2.5 т (:)-т"(т(h) =h Answer: The reciprocal ofthe temperature (in degree Celsius) at a height ofx kilometers

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