Answer :
To determine what [tex]\( C(F) \)[/tex] represents in the context of the given function, we first need to understand the function and its components.
The function is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This formula is used for converting temperatures from degrees Fahrenheit (°F) to degrees Celsius (°C).
Let's break this down:
1. Function Notation [tex]\( C(F) \)[/tex]: Here, [tex]\( C \)[/tex] stands for the degrees Celsius. The function [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after the conversion from Fahrenheit.
2. Input and Calculation:
- The input [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- The function processes this input by first subtracting 32 from [tex]\( F \)[/tex]. This is because the conversion needs to offset the Fahrenheit scale to the Celsius scale.
- Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex]. This step scales the difference from step 1 to convert it appropriately to the Celsius scale.
3. Output [tex]\( C(F) \)[/tex]: The outcome of the function is the temperature in degrees Celsius. Thus, [tex]\( C(F) \)[/tex] is the output of the function in degrees Celsius.
From this analysis, we can say that:
- [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.
Therefore, the correct interpretation or representation 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.
The function is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This formula is used for converting temperatures from degrees Fahrenheit (°F) to degrees Celsius (°C).
Let's break this down:
1. Function Notation [tex]\( C(F) \)[/tex]: Here, [tex]\( C \)[/tex] stands for the degrees Celsius. The function [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after the conversion from Fahrenheit.
2. Input and Calculation:
- The input [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- The function processes this input by first subtracting 32 from [tex]\( F \)[/tex]. This is because the conversion needs to offset the Fahrenheit scale to the Celsius scale.
- Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex]. This step scales the difference from step 1 to convert it appropriately to the Celsius scale.
3. Output [tex]\( C(F) \)[/tex]: The outcome of the function is the temperature in degrees Celsius. Thus, [tex]\( C(F) \)[/tex] is the output of the function in degrees Celsius.
From this analysis, we can say that:
- [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.
Therefore, the correct interpretation or representation 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.