Answer :
Sure! Let's break down the problem and find the correct meaning of [tex]\( C(F) \)[/tex] in the context of converting temperatures from Fahrenheit to Celsius.
The function provided is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
1. Understanding the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The function [tex]\( C(F) \)[/tex] calculates the equivalent temperature in degrees Celsius.
2. Formula Explanation:
- The formula inside the function, [tex]\( \frac{5}{9}(F - 32) \)[/tex], is used to convert a temperature given in Fahrenheit to Celsius.
- It subtracts 32 from [tex]\( F \)[/tex] because this is the freezing point of water in Fahrenheit, and multiplies by [tex]\( \frac{5}{9} \)[/tex] to account for the scaling difference between Fahrenheit and Celsius degrees.
3. Meaning of [tex]\( C(F) \)[/tex]:
- Since [tex]\( C(F) \)[/tex] represents the result after converting [tex]\( F \)[/tex] (degrees Fahrenheit) into degrees Celsius, it means:
- [tex]\( C(F) \)[/tex] is the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
4. Answer Selection:
- Given the options:
- Option 1: [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.
- Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- The correct choice is Option 1 because it accurately describes that [tex]\( C(F) \)[/tex] gives the temperature in Celsius given the Fahrenheit temperature [tex]\( F \)[/tex].
So, the correct interpretation of [tex]\( C(F) \)[/tex] is that it represents the temperature in degrees Celsius when the input temperature is in degrees Fahrenheit.
The function provided is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
1. Understanding the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The function [tex]\( C(F) \)[/tex] calculates the equivalent temperature in degrees Celsius.
2. Formula Explanation:
- The formula inside the function, [tex]\( \frac{5}{9}(F - 32) \)[/tex], is used to convert a temperature given in Fahrenheit to Celsius.
- It subtracts 32 from [tex]\( F \)[/tex] because this is the freezing point of water in Fahrenheit, and multiplies by [tex]\( \frac{5}{9} \)[/tex] to account for the scaling difference between Fahrenheit and Celsius degrees.
3. Meaning of [tex]\( C(F) \)[/tex]:
- Since [tex]\( C(F) \)[/tex] represents the result after converting [tex]\( F \)[/tex] (degrees Fahrenheit) into degrees Celsius, it means:
- [tex]\( C(F) \)[/tex] is the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
4. Answer Selection:
- Given the options:
- Option 1: [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.
- Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- The correct choice is Option 1 because it accurately describes that [tex]\( C(F) \)[/tex] gives the temperature in Celsius given the Fahrenheit temperature [tex]\( F \)[/tex].
So, the correct interpretation of [tex]\( C(F) \)[/tex] is that it represents the temperature in degrees Celsius when the input temperature is in degrees Fahrenheit.