Question

Deon is walking. D(t), given below, is his distance in kilometers from Tomsville after t hours of walking. D(t) = 15.5 - 5t Complete the following statements. Let D^-1 be the inverse function of D. Take x to be an output of the function D. (a) Which statement best describes D^-1(x)? The amount of time he has walked (in hours) when he is x kilometers from Tomsville. His distance from Tomsville (in kilometers) after he has walked x hours. The ratio of the amount of time he has walked (in hours) to his distance from Tomsville (in kilometers), x. The reciprocal of his distance from Tomsville (in kilometers) after walking x hours. (b) D^-1(x) = (c) D^-1(8.5) =

          Deon is walking. D(t), given below, is his distance in kilometers from Tomsville after t hours of walking.
D(t) = 15.5 - 5t
Complete the following statements.
Let D^-1 be the inverse function of D. Take x to be an output of the function D.
(a) Which statement best describes D^-1(x)?
The amount of time he has walked (in hours) when he is x kilometers from Tomsville.
His distance from Tomsville (in kilometers) after he has walked x hours.
The ratio of the amount of time he has walked (in hours) to his distance from Tomsville (in kilometers), x.
The reciprocal of his distance from Tomsville (in kilometers) after walking x hours.
(b) D^-1(x) = 
(c) D^-1(8.5) =

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Deon is walking. D(t), given below, is his distance in kilometers from Tomsville after t hours of walking.
D(t) = 15.5 - 5t
Complete the following statements.
Let D^-1 be the inverse function of D. Take x to be an output of the function D.
(a) Which statement best describes D^-1(x)?
The amount of time he has walked (in hours) when he is x kilometers from Tomsville.
His distance from Tomsville (in kilometers) after he has walked x hours.
The ratio of the amount of time he has walked (in hours) to his distance from Tomsville (in kilometers), x.
The reciprocal of his distance from Tomsville (in kilometers) after walking x hours.
(b) D^-1(x) =
(c) D^-1(8.5) =

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Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Chapman Howard

04/26/2022

Step 1

So, we have D^(-1)(k) = t, where k represents the distance from Tomsville and t represents the amount of time Deon has walked. Show more…

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Deon is walking. D(t), given below, is his distance in kilometers from Tomsville after t hours of walking. D(t) = 15.5 - 5t Complete the following statements. Let D^-1 be the inverse function of D. Take x to be an output of the function D. (a) Which statement best describes D^-1(x)? The amount of time he has walked (in hours) when he is x kilometers from Tomsville. His distance from Tomsville (in kilometers) after he has walked x hours. The ratio of the amount of time he has walked (in hours) to his distance from Tomsville (in kilometers), x. The reciprocal of his distance from Tomsville (in kilometers) after walking x hours. (b) D^-1(x) = (c) D^-1(8.5) =

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Transcript

00:01 So we have a function to model the distance away from some place that dion is walking.

00:06 So this is a function where we input time and output distance from tom'sville.

00:20 That means that the inverse function is going to do the opposite.

00:24 We're going to input distance from tom'sville, and we're going to output time.

00:33 And we need to make sure we formulate that the right way.

00:37 D of t is telling us at time t, what is our distance from tom'sville? t inverse of t is telling us that what distance from tom'sville, or at what time will we be a certain distance from tom'sville.

00:54 So we input, let's say we five kilometers and output how much time it's going to take to walk to the point where we are five kilometers from tom'sville.

01:06 So on these answer choices we have, we want one where we input distance and output time.

01:16 It looks like a is the right choice.

01:21 Yep.

01:22 For b, we want to find the explicit inverse function.

01:27 Well, we know first if we input something, we would need to divide by negative 5 and then subtract 15 .5.

01:36 So the inverse of, i guess we're using x, should be x over minus x over 5 .5, minus 15 .5.

01:57 And we can check this d inverse of d of t.

02:02 It's d inverse.

02:13 And we have made a mistake here.

02:22 It's going to be minus x plus 15...

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