Answer :
Certainly! Let's go through the options to understand what [tex]\( C(F) \)[/tex] represents in this context.
You are given the function:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function converts temperatures from degrees Fahrenheit (denoted by [tex]\( F \)[/tex]) to degrees Celsius (denoted by [tex]\( C(F) \)[/tex]).
Let's analyze each option to see which one correctly describes the function:
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.
- In this option, the function [tex]\( C(F) \)[/tex] receives an input in degrees Fahrenheit (which matches the variable [tex]\( F \)[/tex]) and converts it to degrees Celsius (indicating [tex]\( C(F) \)[/tex]).
- This description is accurate because the formula provided converts Fahrenheit to Celsius.
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.
- Here, this option suggests that the function [tex]\( F \)[/tex] is converting from Celsius to Fahrenheit, which is not what is happening. The function [tex]\( C(F) \)[/tex] we have converts Fahrenheit to Celsius, not the other way around.
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.
- This option suggests the conversion from Celsius to Fahrenheit, which is incorrect. Again, our given function takes Fahrenheit as input and gives Celsius as output.
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.
- This option does not correctly describe the relationship. It incorrectly mentions the function [tex]\( F \)[/tex] and suggests input in Celsius, which is not the process described by [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
Based on the above analysis, the correct choice 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. This matches the description of the function given for converting temperature from Fahrenheit to Celsius.
You are given the function:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function converts temperatures from degrees Fahrenheit (denoted by [tex]\( F \)[/tex]) to degrees Celsius (denoted by [tex]\( C(F) \)[/tex]).
Let's analyze each option to see which one correctly describes the function:
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.
- In this option, the function [tex]\( C(F) \)[/tex] receives an input in degrees Fahrenheit (which matches the variable [tex]\( F \)[/tex]) and converts it to degrees Celsius (indicating [tex]\( C(F) \)[/tex]).
- This description is accurate because the formula provided converts Fahrenheit to Celsius.
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.
- Here, this option suggests that the function [tex]\( F \)[/tex] is converting from Celsius to Fahrenheit, which is not what is happening. The function [tex]\( C(F) \)[/tex] we have converts Fahrenheit to Celsius, not the other way around.
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.
- This option suggests the conversion from Celsius to Fahrenheit, which is incorrect. Again, our given function takes Fahrenheit as input and gives Celsius as output.
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.
- This option does not correctly describe the relationship. It incorrectly mentions the function [tex]\( F \)[/tex] and suggests input in Celsius, which is not the process described by [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
Based on the above analysis, the correct choice 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. This matches the description of the function given for converting temperature from Fahrenheit to Celsius.