EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
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Chapter 3.4, Problem 48PS
Solution

(a)

Find the inverse of the given model. Describe what information you can obtain from the inverse.

  C1=9F5+32

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was 10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

The inverse of C=59(F32) is -

  C=59(F32)y=Cy=59(F32)swapFwithyF=59(y32)solveforyF=59(y32)9F=5(y32)9F5=y32y=9F5+32C1=9F5+32

Thus the inverse of the given function C=59(F32) is C1=9F5+32 .

From the inverse we obtained that adding 32 with 9/5 times Fahrenheit (F) temperature gives the degree Celsius (C) temperature.

(b)

Find the Fahrenheit temperatures at the start and end of the race.

Fahrenheit temperatures at the start F=410

Fahrenheit temperatures at the end F=140

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was 10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

  C=59(F32)

At the start the temperature was 5oC .

Fahrenheit temperatures at the start −

  C=59(F32)5=59(F32)9=F32F=9+32F=410

At the end the temperature was 10oC .

Fahrenheit temperatures at the start −

  C=59(F32)10=59(F32)905=F3218=F32F=3218F=14o

(c)

Use a graphic calculator to graph the original function and its inverse. Find the temperature that is the same on both temperature scales.

At -40 both temperature scales are same, C=F=40o

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was 10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

The graph of C=59(F32) and C1=9F5+32 is-

  EBK ALGEBRA 2, Chapter 3.4, Problem 48PS

At 40o the temperature is same on both temperature scales.

  C=F=40

  C=59(F32)40=59(4032)360=5(72)360=360

Chapter 3 Solutions

EBK ALGEBRA 2

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