Answer :
Sure! Let's go through the problem step-by-step to understand what [tex]\( C(F) \)[/tex] represents.
1. Understanding the Function: The function given is [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex]. This is a standard mathematical formula used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
2. Identifying the Components:
- [tex]\( F \)[/tex] is the input to the function, representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which gives us the temperature in degrees Celsius once the conversion is done.
3. What Does [tex]\( C(F) \)[/tex] Represent?: Since the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] converts a given temperature from Fahrenheit to Celsius, the output value, [tex]\( C(F) \)[/tex], is in degrees Celsius.
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.
This matches the first interpretation provided: [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. Understanding the Function: The function given is [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex]. This is a standard mathematical formula used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
2. Identifying the Components:
- [tex]\( F \)[/tex] is the input to the function, representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which gives us the temperature in degrees Celsius once the conversion is done.
3. What Does [tex]\( C(F) \)[/tex] Represent?: Since the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] converts a given temperature from Fahrenheit to Celsius, the output value, [tex]\( C(F) \)[/tex], is in degrees Celsius.
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.
This matches the first interpretation provided: [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.