Answer :
To convert temperatures from degrees Fahrenheit to degrees Celsius, we use the function [tex]\( C(f) = \frac{5}{9}(f - 32) \)[/tex].
In this function:
- [tex]\( f \)[/tex] is the temperature in degrees Fahrenheit that you want to convert.
- [tex]\( C(f) \)[/tex] is the result of the conversion and it gives you the temperature in degrees Celsius.
Let's break down the function:
1. Subtract 32: The formula starts by taking the Fahrenheit temperature and subtracting 32 from it. This is because 32 degrees Fahrenheit corresponds to the freezing point of water, which is 0 degrees Celsius.
2. Multiply by [tex]\(\frac{5}{9}\)[/tex]: After subtracting 32, you multiply the result by [tex]\(\frac{5}{9}\)[/tex]. This fraction is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
When we interpret what [tex]\( C(F) \)[/tex] represents:
- Input [tex]\( F \)[/tex]: This is the temperature value you plug into the function, given in degrees Fahrenheit.
- Output [tex]\( C(f) \)[/tex]: This is the result you get after performing the calculation, giving the temperature in degrees Celsius.
Thus, [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 means the correct interpretation of [tex]\( C(F) \)[/tex] is that it is the value of the temperature conversion from Fahrenheit to Celsius.
In summary, the correct answer 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.
In this function:
- [tex]\( f \)[/tex] is the temperature in degrees Fahrenheit that you want to convert.
- [tex]\( C(f) \)[/tex] is the result of the conversion and it gives you the temperature in degrees Celsius.
Let's break down the function:
1. Subtract 32: The formula starts by taking the Fahrenheit temperature and subtracting 32 from it. This is because 32 degrees Fahrenheit corresponds to the freezing point of water, which is 0 degrees Celsius.
2. Multiply by [tex]\(\frac{5}{9}\)[/tex]: After subtracting 32, you multiply the result by [tex]\(\frac{5}{9}\)[/tex]. This fraction is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
When we interpret what [tex]\( C(F) \)[/tex] represents:
- Input [tex]\( F \)[/tex]: This is the temperature value you plug into the function, given in degrees Fahrenheit.
- Output [tex]\( C(f) \)[/tex]: This is the result you get after performing the calculation, giving the temperature in degrees Celsius.
Thus, [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 means the correct interpretation of [tex]\( C(F) \)[/tex] is that it is the value of the temperature conversion from Fahrenheit to Celsius.
In summary, the correct answer 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.