Answer :
To solve this problem, we need to understand what [tex]$C(F)$[/tex] represents in the context of the function given, which is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Let's break down what each part of this function is doing:
1. Input: The function takes an input [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
2. Operation:
- First, it subtracts 32 from the Fahrenheit temperature. This adjusts the temperature measurement because the freezing point of water is 32 degrees Fahrenheit and 0 degrees Celsius.
- Then, it multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This is a conversion factor that changes the scale from Fahrenheit to Celsius.
3. Output: The result of these operations [tex]\( C(F) \)[/tex] is the temperature converted into degrees Celsius.
Understanding this, we conclude that:
- [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.
So the correct interpretation 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 function is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Let's break down what each part of this function is doing:
1. Input: The function takes an input [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
2. Operation:
- First, it subtracts 32 from the Fahrenheit temperature. This adjusts the temperature measurement because the freezing point of water is 32 degrees Fahrenheit and 0 degrees Celsius.
- Then, it multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This is a conversion factor that changes the scale from Fahrenheit to Celsius.
3. Output: The result of these operations [tex]\( C(F) \)[/tex] is the temperature converted into degrees Celsius.
Understanding this, we conclude that:
- [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.
So the correct interpretation 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.