Answer :
To solve the question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing. This function is converting temperatures from degrees Fahrenheit to degrees Celsius.
Let's break it down step-by-step:
1. Function Interpretation:
- The function [tex]\( C(F) \)[/tex] is used to convert an input temperature from Fahrenheit to Celsius.
2. Function Explanation:
- The variable [tex]\( F \)[/tex] represents the temperature input in degrees Fahrenheit.
- The expression [tex]\( (F - 32) \)[/tex] converts the Fahrenheit value to a scale that is easier to convert to Celsius by subtracting 32, which is the freezing point of water in Fahrenheit.
- The multiplication by [tex]\( \frac{5}{9} \)[/tex] accounts for the difference in the size of degrees between the Fahrenheit and Celsius scales, effectively converting the adjusted Fahrenheit value to Celsius.
3. Function Output:
- The output [tex]\( C(F) \)[/tex] gives the converted temperature in degrees Celsius.
- So, [tex]\( C(F) \)[/tex] means the temperature in Celsius after converting from the Fahrenheit input.
Now, based on this explanation, the correct interpretation of [tex]\( C(F) \)[/tex] from the given options 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 option correctly describes the conversion function's role and how it translates temperatures between the two scales.
Let's break it down step-by-step:
1. Function Interpretation:
- The function [tex]\( C(F) \)[/tex] is used to convert an input temperature from Fahrenheit to Celsius.
2. Function Explanation:
- The variable [tex]\( F \)[/tex] represents the temperature input in degrees Fahrenheit.
- The expression [tex]\( (F - 32) \)[/tex] converts the Fahrenheit value to a scale that is easier to convert to Celsius by subtracting 32, which is the freezing point of water in Fahrenheit.
- The multiplication by [tex]\( \frac{5}{9} \)[/tex] accounts for the difference in the size of degrees between the Fahrenheit and Celsius scales, effectively converting the adjusted Fahrenheit value to Celsius.
3. Function Output:
- The output [tex]\( C(F) \)[/tex] gives the converted temperature in degrees Celsius.
- So, [tex]\( C(F) \)[/tex] means the temperature in Celsius after converting from the Fahrenheit input.
Now, based on this explanation, the correct interpretation of [tex]\( C(F) \)[/tex] from the given options 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 option correctly describes the conversion function's role and how it translates temperatures between the two scales.