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:
1. Identify the Variables:
- [tex]\( F \)[/tex] represents a temperature in degrees Fahrenheit. This is the input of the function.
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. This is a standard formula for temperature conversion.
3. Apply the Mathematical Operation:
- Subtract 32 from the Fahrenheit temperature ([tex]\( F \)[/tex]). This adjusts the input correctly as 32°F is the freezing point of water and is used as a baseline in the conversion.
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This scales down the adjusted temperature from Fahrenheit to Celsius, as there are 5 Celsius degrees for every 9 Fahrenheit degrees.
4. Interpret the Output:
- The result of the function, [tex]\( C(F) \)[/tex], will give the corresponding temperature in degrees Celsius.
5. Conclusion:
- Therefore, [tex]\( C(F) \)[/tex] represents the output of the function in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This means 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] represents a temperature in degrees Fahrenheit. This is the input of the function.
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. This is a standard formula for temperature conversion.
3. Apply the Mathematical Operation:
- Subtract 32 from the Fahrenheit temperature ([tex]\( F \)[/tex]). This adjusts the input correctly as 32°F is the freezing point of water and is used as a baseline in the conversion.
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This scales down the adjusted temperature from Fahrenheit to Celsius, as there are 5 Celsius degrees for every 9 Fahrenheit degrees.
4. Interpret the Output:
- The result of the function, [tex]\( C(F) \)[/tex], will give the corresponding temperature in degrees Celsius.
5. Conclusion:
- Therefore, [tex]\( C(F) \)[/tex] represents the output of the function in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This means 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.