Answer :
To understand the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], let's break it down step by step:
1. Input and Output: The function [tex]\( C(F) \)[/tex] is used to convert a temperature from Fahrenheit to Celsius. In this expression:
- [tex]\( F \)[/tex] is the input, representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, representing the temperature in degrees Celsius.
2. Understanding the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is the mathematical representation used to convert Fahrenheit to Celsius.
- The part [tex]\( (F-32) \)[/tex] translates the Fahrenheit temperature to account for the offset between the two scales.
- The fraction [tex]\( \frac{5}{9} \)[/tex] is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
3. Conversion Process:
- Subtract 32 from the Fahrenheit temperature. This is the first step to offset the starting points of the two temperature scales (since 32°F is equivalent to 0°C).
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This adjusts the temperature difference from the Fahrenheit scale to the Celsius scale, which is a smaller unit increment.
4. Function Representation:
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius when you have the temperature in degrees Fahrenheit as the input.
Finally, putting all of this understanding together, we conclude:
[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 the purpose of using the formula to perform the temperature conversion.
1. Input and Output: The function [tex]\( C(F) \)[/tex] is used to convert a temperature from Fahrenheit to Celsius. In this expression:
- [tex]\( F \)[/tex] is the input, representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, representing the temperature in degrees Celsius.
2. Understanding the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is the mathematical representation used to convert Fahrenheit to Celsius.
- The part [tex]\( (F-32) \)[/tex] translates the Fahrenheit temperature to account for the offset between the two scales.
- The fraction [tex]\( \frac{5}{9} \)[/tex] is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
3. Conversion Process:
- Subtract 32 from the Fahrenheit temperature. This is the first step to offset the starting points of the two temperature scales (since 32°F is equivalent to 0°C).
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This adjusts the temperature difference from the Fahrenheit scale to the Celsius scale, which is a smaller unit increment.
4. Function Representation:
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius when you have the temperature in degrees Fahrenheit as the input.
Finally, putting all of this understanding together, we conclude:
[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 the purpose of using the formula to perform the temperature conversion.