Answer :
To solve this problem and understand what [tex]$C(F)$[/tex] represents, we need to analyze the function provided:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This is a well-known formula used to convert temperatures from degrees Fahrenheit to degrees Celsius. Here's a breakdown of the process:
1. Understanding the Conversion Formula:
- The expression [tex]\((F - 32)\)[/tex] adjusts the Fahrenheit temperature by accounting for the offset in the freezing point between Fahrenheit and Celsius scales. On the Fahrenheit scale, water freezes at 32 degrees, whereas on the Celsius scale, it freezes at 0 degrees.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is used to scale the temperature difference from Fahrenheit to Celsius. Since the Fahrenheit scale progresses faster than Celsius (180 units between freezing and boiling for Fahrenheit versus 100 for Celsius), this fraction accounts for that ratio of 180/100, simplified to 9/5.
2. Interpreting the Function:
- Input (F): The function takes an input [tex]\(F\)[/tex], which is the temperature in degrees Fahrenheit.
- Output (C(F)): The output of the function [tex]\(C(F)\)[/tex] is the temperature converted to degrees Celsius.
3. Choice Explanation:
- The correct choice must reflect that the function takes a Fahrenheit input and converts it to Celsius.
- Therefore, the statement that accurately describes [tex]\(C(F)\)[/tex] is: "C(F) represents the output of the function [tex]\(C\)[/tex] in degrees Celsius when the input [tex]\(F\)[/tex] is in degrees Fahrenheit."
Based on this explanation, we can conclude that [tex]$C(F)$[/tex] indeed stands for the temperature in degrees Celsius after converting from degrees Fahrenheit, when following the given formula.
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This is a well-known formula used to convert temperatures from degrees Fahrenheit to degrees Celsius. Here's a breakdown of the process:
1. Understanding the Conversion Formula:
- The expression [tex]\((F - 32)\)[/tex] adjusts the Fahrenheit temperature by accounting for the offset in the freezing point between Fahrenheit and Celsius scales. On the Fahrenheit scale, water freezes at 32 degrees, whereas on the Celsius scale, it freezes at 0 degrees.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is used to scale the temperature difference from Fahrenheit to Celsius. Since the Fahrenheit scale progresses faster than Celsius (180 units between freezing and boiling for Fahrenheit versus 100 for Celsius), this fraction accounts for that ratio of 180/100, simplified to 9/5.
2. Interpreting the Function:
- Input (F): The function takes an input [tex]\(F\)[/tex], which is the temperature in degrees Fahrenheit.
- Output (C(F)): The output of the function [tex]\(C(F)\)[/tex] is the temperature converted to degrees Celsius.
3. Choice Explanation:
- The correct choice must reflect that the function takes a Fahrenheit input and converts it to Celsius.
- Therefore, the statement that accurately describes [tex]\(C(F)\)[/tex] is: "C(F) represents the output of the function [tex]\(C\)[/tex] in degrees Celsius when the input [tex]\(F\)[/tex] is in degrees Fahrenheit."
Based on this explanation, we can conclude that [tex]$C(F)$[/tex] indeed stands for the temperature in degrees Celsius after converting from degrees Fahrenheit, when following the given formula.