Answer :
Sure, let's break down the question step-by-step to understand what [tex]$C(F)$[/tex] represents.
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
### Step 1: Understanding the Function
- [tex]\( C(F) \)[/tex]: This is the function notation. Here, [tex]\( C \)[/tex] is the function that takes an input [tex]\( F \)[/tex].
- [tex]\( F \)[/tex]: This represents the temperature in degrees Fahrenheit. It's the input to the function.
- [tex]\( C(F) \)[/tex]: This is the output of the function, representing what you'll find when you input [tex]\( F \)[/tex] into the function.
### Step 2: What Does the Function Do?
The function converts a temperature from Fahrenheit to Celsius. It does so by:
- Subtracting 32 from the Fahrenheit temperature ([tex]\( F - 32 \)[/tex]).
- Multiplying the result by [tex]\( \frac{5}{9} \)[/tex].
This is a standard formula to convert Fahrenheit to Celsius.
### Step 3: What Does [tex]\( C(F) \)[/tex] Represent?
From the function, we can see:
- The input [tex]\( F \)[/tex] is in degrees Fahrenheit.
- The expression [tex]\(\frac{5}{9}(F - 32)\)[/tex] gives us the temperature in degrees Celsius.
Therefore, [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex], which is the temperature in degrees Celsius after converting it from Fahrenheit.
### Conclusion
Based on this understanding, 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.
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
### Step 1: Understanding the Function
- [tex]\( C(F) \)[/tex]: This is the function notation. Here, [tex]\( C \)[/tex] is the function that takes an input [tex]\( F \)[/tex].
- [tex]\( F \)[/tex]: This represents the temperature in degrees Fahrenheit. It's the input to the function.
- [tex]\( C(F) \)[/tex]: This is the output of the function, representing what you'll find when you input [tex]\( F \)[/tex] into the function.
### Step 2: What Does the Function Do?
The function converts a temperature from Fahrenheit to Celsius. It does so by:
- Subtracting 32 from the Fahrenheit temperature ([tex]\( F - 32 \)[/tex]).
- Multiplying the result by [tex]\( \frac{5}{9} \)[/tex].
This is a standard formula to convert Fahrenheit to Celsius.
### Step 3: What Does [tex]\( C(F) \)[/tex] Represent?
From the function, we can see:
- The input [tex]\( F \)[/tex] is in degrees Fahrenheit.
- The expression [tex]\(\frac{5}{9}(F - 32)\)[/tex] gives us the temperature in degrees Celsius.
Therefore, [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex], which is the temperature in degrees Celsius after converting it from Fahrenheit.
### Conclusion
Based on this understanding, 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.