Answer :
To solve the question of what the function [tex]\( C(F) \)[/tex] represents, we first need to understand the function itself. The function given is:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
This function is used to convert temperatures from degrees Fahrenheit (°F) to degrees Celsius (°C).
Here's a step-by-step breakdown:
1. Identify the function and its purpose:
- The function [tex]\( C(F) \)[/tex] is defined to convert the input temperature in Fahrenheit (denoted as [tex]\( F \)[/tex]) into a temperature in Celsius.
- The formula [tex]\( C(F) = \frac{5}{9} (F - 32) \)[/tex] is a standard conversion formula where you subtract 32 from the Fahrenheit temperature and multiply the result by [tex]\(\frac{5}{9}\)[/tex].
2. Understand the variables involved:
- [tex]\( F \)[/tex] is the input variable representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which will be the temperature in degrees Celsius after conversion.
3. Interpret what [tex]\( C(F) \)[/tex] represents:
- Since the formula converts a temperature from Fahrenheit to Celsius, [tex]\( C(F) \)[/tex] gives us the result in degrees Celsius.
Thus, 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.
This matches with the first option provided, indicating a clear conversion from Fahrenheit to Celsius.
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
This function is used to convert temperatures from degrees Fahrenheit (°F) to degrees Celsius (°C).
Here's a step-by-step breakdown:
1. Identify the function and its purpose:
- The function [tex]\( C(F) \)[/tex] is defined to convert the input temperature in Fahrenheit (denoted as [tex]\( F \)[/tex]) into a temperature in Celsius.
- The formula [tex]\( C(F) = \frac{5}{9} (F - 32) \)[/tex] is a standard conversion formula where you subtract 32 from the Fahrenheit temperature and multiply the result by [tex]\(\frac{5}{9}\)[/tex].
2. Understand the variables involved:
- [tex]\( F \)[/tex] is the input variable representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which will be the temperature in degrees Celsius after conversion.
3. Interpret what [tex]\( C(F) \)[/tex] represents:
- Since the formula converts a temperature from Fahrenheit to Celsius, [tex]\( C(F) \)[/tex] gives us the result in degrees Celsius.
Thus, 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.
This matches with the first option provided, indicating a clear conversion from Fahrenheit to Celsius.