Answer :
To understand what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], let’s break it down step by step:
1. Identify the Variables:
- [tex]\( F \)[/tex] is the input of the function, which stands for the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which we'll determine.
2. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
3. Interpret the Expression:
- The formula [tex]\( \frac{5}{9}(F-32) \)[/tex] is commonly used in temperature conversion from Fahrenheit to Celsius. It takes the Fahrenheit temperature [tex]\( F \)[/tex], subtracts 32, and then multiplies the result by [tex]\( \frac{5}{9} \)[/tex].
4. Determine [tex]\( C(F) \)[/tex]:
- Since the function takes [tex]\( F \)[/tex] (degrees Fahrenheit) and converts it to degrees Celsius, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
5. Conclusion:
- Therefore, [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.
With these steps, we conclude that the correct interpretation 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.
1. Identify the Variables:
- [tex]\( F \)[/tex] is the input of the function, which stands for the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which we'll determine.
2. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
3. Interpret the Expression:
- The formula [tex]\( \frac{5}{9}(F-32) \)[/tex] is commonly used in temperature conversion from Fahrenheit to Celsius. It takes the Fahrenheit temperature [tex]\( F \)[/tex], subtracts 32, and then multiplies the result by [tex]\( \frac{5}{9} \)[/tex].
4. Determine [tex]\( C(F) \)[/tex]:
- Since the function takes [tex]\( F \)[/tex] (degrees Fahrenheit) and converts it to degrees Celsius, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
5. Conclusion:
- Therefore, [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.
With these steps, we conclude that the correct interpretation 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.