Answer :
To solve this problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing. This function is applied to convert a temperature given in degrees Fahrenheit (F) to degrees Celsius (C).
Here's how the function works, step-by-step:
1. Identify the Input and Output:
- The input to the function [tex]\( C(F) \)[/tex] is a temperature in degrees Fahrenheit, represented by [tex]\( F \)[/tex].
- The output of the function is a temperature in degrees Celsius, represented by [tex]\( C(F) \)[/tex].
2. Understand the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard conversion formula.
- It takes the Fahrenheit temperature [tex]\( F \)[/tex], subtracts 32 from it, multiplies the result by [tex]\(\frac{5}{9}\)[/tex], and returns the equivalent temperature in Celsius.
3. Interpret the Meaning of [tex]\( C(F) \)[/tex]:
- Since the function is converting from Fahrenheit to Celsius, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after the conversion process when the input is in degrees Fahrenheit.
Based on the explanation above, let's evaluate each option to identify the correct one:
- Option 1: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This option correctly matches our understanding of the conversion function.
- Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
This is not correct because the function does not convert Celsius to Fahrenheit.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
This is also incorrect because the function outputs Celsius, not Fahrenheit.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
This again is incorrect as the input to the function is in Fahrenheit, and it outputs in Celsius, not the other way around.
Therefore, the correct interpretation and answer is:
Option 1: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
Here's how the function works, step-by-step:
1. Identify the Input and Output:
- The input to the function [tex]\( C(F) \)[/tex] is a temperature in degrees Fahrenheit, represented by [tex]\( F \)[/tex].
- The output of the function is a temperature in degrees Celsius, represented by [tex]\( C(F) \)[/tex].
2. Understand the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard conversion formula.
- It takes the Fahrenheit temperature [tex]\( F \)[/tex], subtracts 32 from it, multiplies the result by [tex]\(\frac{5}{9}\)[/tex], and returns the equivalent temperature in Celsius.
3. Interpret the Meaning of [tex]\( C(F) \)[/tex]:
- Since the function is converting from Fahrenheit to Celsius, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after the conversion process when the input is in degrees Fahrenheit.
Based on the explanation above, let's evaluate each option to identify the correct one:
- Option 1: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This option correctly matches our understanding of the conversion function.
- Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
This is not correct because the function does not convert Celsius to Fahrenheit.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
This is also incorrect because the function outputs Celsius, not Fahrenheit.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
This again is incorrect as the input to the function is in Fahrenheit, and it outputs in Celsius, not the other way around.
Therefore, the correct interpretation and answer is:
Option 1: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.