Answer :
To solve this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is meant to do. Let's break it down step-by-step:
1. Identify the Purpose of the Function:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit (denoted as [tex]\( F \)[/tex]) to degrees Celsius (denoted as [tex]\( C \, (F) \)[/tex]).
2. Understanding the Terms:
- Here, [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius after the conversion using the formula.
3. Interpret the Function:
- When you input a temperature [tex]\( F \)[/tex] in degrees Fahrenheit into the function [tex]\( C(F) \)[/tex], the function converts it to a value representing the same temperature in degrees Celsius.
4. Choose the Correct Interpretation:
- We have different statements explaining what [tex]\( C(F) \)[/tex] represents:
- The correct statement is: "[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 choice correctly explains the function's purpose, which is to convert temperatures from Fahrenheit to Celsius. The other options do not accurately describe the relationship between Fahrenheit and Celsius as given by this formula.
1. Identify the Purpose of the Function:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit (denoted as [tex]\( F \)[/tex]) to degrees Celsius (denoted as [tex]\( C \, (F) \)[/tex]).
2. Understanding the Terms:
- Here, [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius after the conversion using the formula.
3. Interpret the Function:
- When you input a temperature [tex]\( F \)[/tex] in degrees Fahrenheit into the function [tex]\( C(F) \)[/tex], the function converts it to a value representing the same temperature in degrees Celsius.
4. Choose the Correct Interpretation:
- We have different statements explaining what [tex]\( C(F) \)[/tex] represents:
- The correct statement is: "[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 choice correctly explains the function's purpose, which is to convert temperatures from Fahrenheit to Celsius. The other options do not accurately describe the relationship between Fahrenheit and Celsius as given by this formula.