Respuesta :
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
The statement that best describes T^-1(x) is (b) The height above the surface (in kilometers) when the temperature is x degrees Celsius.
The function is given as:
[tex]\mathbf{T(h)= 30.5 - 2.5h}[/tex]
And it represents the temperature at a given height h.
The inverse function T^-1 would represent the height, given the temperature.
So, the statement that best describes T^-1(x) is (b)
We have:
[tex]\mathbf{T(h)= 30.5 - 2.5h}[/tex]
Rewrite as:
[tex]\mathbf{T= 30.5 - 2.5h}[/tex]
Rewrite as:
[tex]\mathbf{2.5h= 30.5 - T}[/tex]
Divide both sides by 2.5
[tex]\mathbf{h= \frac{30.5}{2.5} - \frac{T}{2.5}}[/tex]
[tex]\mathbf{h= 12.2 - 0.4T}[/tex]
Represent T with x
[tex]\mathbf{h= 12.2 - 0.4x}[/tex]
So, we have:
[tex]\mathbf{T^{-1}(x)= 12.2 - 0.4x}[/tex]
Substitute 15 for x
[tex]\mathbf{T^{-1}(15)= 12.2 - 0.4 \times 15 }[/tex]
[tex]\mathbf{T^{-1}(15)= 6.2}[/tex]
Read more about inverse functions at:
https://brainly.com/question/10300045
