Teresa is walking. D(t), given below, is her distance in kilometers from Glenn City after t hours of walking.

D(t) = 10.4 - 4t

a) Which statement best describes D^-1(x)?
a. The amount of time she has walked (in hours) when she is x kilometers from Glenn City
b. The reciprocal of her distance from Glenn City (In Kilometers) after walking x hours.
c. Her distance from Glenn City (in kilometers) after she has walked x hours.
d. The ratio of the amount of time she has walked (in hours) to her distance from Glen City (in kilometers) x.

b) D^-1(x) =

c) D^-1(5.2) =

D(t) = Teresa's distance in kilometers from Glenn City after t hours of walking. The inverse of this would be the time she has walked about x kilometers.

(b)

D(t) = 10.4 - 4t

Change t to x --> y = 10.4 - 4x

Switch x and y --> x = 10.4 - 4y

Solve for y:

D^-1(x) = x - 10.4 = -4y

[tex]\frac{x-10.4}{-4} =\frac{y}{-4}[/tex]

D^-1(x) = (x-10.4)/-4

(c)

Insert 5.2 where x is:

(5.2 - 10.4) / 4 = -1.3

MrRoyal MrRoyal · Answer 2 · 2021-10-12T13:12:31+02:00

All functions must have an inverse function.

[tex]\mathbf{D^{-1}(t)}[/tex] represents the amount of time she has walked (in hours) when she is x kilometers from Glenn City
The inverse function is: [tex]\mathbf{D^{-1}(t) = \frac{10.4 - t}{4}}[/tex]
[tex]\mathbf{D^{-1}(5.2) = 1.3}[/tex]

The function is given as:

[tex]\mathbf{D(t) = 10.4 - 4t}[/tex]

The above function calculates the distance Teresa has walked, given the number of hours

So, the inverse function [tex]\mathbf{D^{-1}(t)}[/tex] would calculate the time, from the distance.

This means that, [tex]\mathbf{D^{-1}(t)}[/tex] represents

a. The amount of time she has walked (in hours) when she is x kilometers from Glenn City

To calculate the inverse function, we have:

[tex]\mathbf{D(t) = 10.4 - 4t}[/tex]

Rewrite as:

[tex]\mathbf{D = 10.4 - 4t}[/tex]

Subtract 10.4 from both sides

[tex]\mathbf{D - 10.4 =- 4t}[/tex]

Divide both sides by -4

[tex]\mathbf{t = \frac{10.4 - D}{4}}[/tex]

Rewrite as:

[tex]\mathbf{D^{-1}(t) = \frac{10.4 - t}{4}}[/tex]

Hence, the inverse function is: [tex]\mathbf{D^{-1}(t) = \frac{10.4 - t}{4}}[/tex]

Substitute 5.2 for t to calculate [tex]\mathbf{D^{-1}(5.2)}[/tex]

[tex]\mathbf{D^{-1}(5.2) = \frac{10.4 - 5.2}{4}}[/tex]

[tex]\mathbf{D^{-1}(5.2) = \frac{5.2}{4}}[/tex]

[tex]\mathbf{D^{-1}(5.2) = 1.3}[/tex]

Read more about inverse functions at:

https://brainly.com/question/10300045