1) Taking into account reaction time, the distance d in feet that a car requires to come to a complete stop while traveling r miles per hour is given by the function. = 7.02r – 86.48 a) What would be the practical domain and range for function d and why? b) Solve for the inverse of d (r). What might you call the inverse? Why would it not make sense in this case to call it d(r)? c) Present d(r) and its inverse; graphically and with a table. Explain how each representation shows the inverse relationship with examples. d) What would be the practical domain and range for the inverse of d? e) Use the graph and equation of the inverse to describe in context what r(300) would mean (I'm calling the inverse function r here). f) How could you algebraically verify that your two functions are in fact inverses?
1) Taking into account reaction time, the distance d in feet that a car requires to come to a complete stop while traveling r miles per hour is given by the function. = 7.02r – 86.48 a) What would be the practical domain and range for function d and why? b) Solve for the inverse of d (r). What might you call the inverse? Why would it not make sense in this case to call it d(r)? c) Present d(r) and its inverse; graphically and with a table. Explain how each representation shows the inverse relationship with examples. d) What would be the practical domain and range for the inverse of d? e) Use the graph and equation of the inverse to describe in context what r(300) would mean (I'm calling the inverse function r here). f) How could you algebraically verify that your two functions are in fact inverses?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Math 111 Focus Set 3
Answer the following questions. Be sure to follow the guidelines for writing Focus Set
responses. See the course page for details if you need a refresher.
1) Taking into account reaction time, the distance d in feet that a car requires to come to a
complete stop while traveling r miles per hour is given by the function.
d(r) = 7.02r – 86.48
%3D
a) What would be the practical domain and range for function d and why?
b) Solve for the inverse of d(r). What might you call the inverse? Why would it not make
sense in this case to call it d(r)?
c) Present d(r) and its inverse; graphically and with a table. Explain how each
representation shows the inverse relationship with examples.
d) What would be the practical domain and range for the inverse of d?
e) Use the graph and equation of the inverse to describe in context what r(300) would
mean (I'm calling the inverse function r here).
f) How could you algebraically verify that your two functions are in fact inverses?
2) Consider the function f and g graphed
here.
a. Express using functions notation how
to transform one of the functions
into the other.
g(x)
f(x)
b. Verify your answer by showing how
one ordered pair goes through the
-5
transformation.
Bonus: Show and explain how to go the
other direction for 2pts extra credit.
-5+
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