Answer :
To understand what [tex]\( C(F) \)[/tex] represents, let's break down the conversion function:
The function given is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Here's how it works:
1. Identify the Parts:
- [tex]\( F \)[/tex] is the input, which is the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, which represents the temperature in degrees Celsius.
2. Subtraction Step:
- The expression [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by removing the offset often used in the conversion formula. This 32 is crucial because 32°F is the point at which water freezes, corresponding to 0°C.
3. Scaling Step:
- The fraction [tex]\(\frac{5}{9}\)[/tex] is a scaling factor that converts the adjusted Fahrenheit value into the Celsius scale. This factor ensures that each degree Fahrenheit is converted to its equivalent in degrees Celsius, based on their respective scales.
4. Overall Conversion:
- The function directly transforms the Fahrenheit input into a Celsius output by combining these steps.
Therefore, based on this breakdown, [tex]\( C(F) \)[/tex] specifically describes the temperature in degrees Celsius once you've inputted the temperature in degrees Fahrenheit.
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.
The function given is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Here's how it works:
1. Identify the Parts:
- [tex]\( F \)[/tex] is the input, which is the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, which represents the temperature in degrees Celsius.
2. Subtraction Step:
- The expression [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by removing the offset often used in the conversion formula. This 32 is crucial because 32°F is the point at which water freezes, corresponding to 0°C.
3. Scaling Step:
- The fraction [tex]\(\frac{5}{9}\)[/tex] is a scaling factor that converts the adjusted Fahrenheit value into the Celsius scale. This factor ensures that each degree Fahrenheit is converted to its equivalent in degrees Celsius, based on their respective scales.
4. Overall Conversion:
- The function directly transforms the Fahrenheit input into a Celsius output by combining these steps.
Therefore, based on this breakdown, [tex]\( C(F) \)[/tex] specifically describes the temperature in degrees Celsius once you've inputted the temperature in degrees Fahrenheit.
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.