Answer :
To solve the question about what [tex]$C(F)$[/tex] represents, we need to understand the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
Here is a step-by-step explanation:
1. Identify the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a conversion formula. It is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Understand the Inputs and Outputs:
- Input: [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- Output: [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
3. Analysis of Function:
- The function takes a temperature value in Fahrenheit (the input [tex]\( F \)[/tex]) and converts it to Celsius (the output [tex]\( C(F) \)[/tex]).
- The formula subtracts 32 from the Fahrenheit temperature, then scales it by [tex]\(\frac{5}{9}\)[/tex] to adjust the temperature into Celsius.
4. What Does [tex]\( C(F) \)[/tex] Represent?:
- Since [tex]\( C(F) \)[/tex] gives us a temperature value in degrees Celsius when we input a temperature in degrees Fahrenheit, it represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] 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.
Here is a step-by-step explanation:
1. Identify the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a conversion formula. It is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Understand the Inputs and Outputs:
- Input: [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- Output: [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
3. Analysis of Function:
- The function takes a temperature value in Fahrenheit (the input [tex]\( F \)[/tex]) and converts it to Celsius (the output [tex]\( C(F) \)[/tex]).
- The formula subtracts 32 from the Fahrenheit temperature, then scales it by [tex]\(\frac{5}{9}\)[/tex] to adjust the temperature into Celsius.
4. What Does [tex]\( C(F) \)[/tex] Represent?:
- Since [tex]\( C(F) \)[/tex] gives us a temperature value in degrees Celsius when we input a temperature in degrees Fahrenheit, it represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] 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.