Answer :
Sure, let's break down the problem to understand what [tex]$C(F)$[/tex] represents.
You're given the function [tex]$C(F)=\frac{5}{9}(F-32)$[/tex], which is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Let's analyze the components of the function step-by-step:
1. Fahrenheit to Celsius Conversion Formula: The general formula to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C) is:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
This formula is used to find the equivalent temperature in degrees Celsius given the temperature in degrees Fahrenheit.
2. Understanding [tex]$C(F)$[/tex]:
- Here, [tex]$C(F)$[/tex] is a function notation where [tex]$C$[/tex] represents the output in degrees Celsius.
- When you substitute a value of [tex]$F$[/tex] (temperature in Fahrenheit) into this function, it converts that Fahrenheit temperature into Celsius.
3. Interpreting the Function:
- [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex], which is in degrees Celsius.
- The input to the function is [tex]$F$[/tex], which is in degrees Fahrenheit.
Thus, the correct interpretation is 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.
Therefore, the first option is correct:
- [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.
You're given the function [tex]$C(F)=\frac{5}{9}(F-32)$[/tex], which is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Let's analyze the components of the function step-by-step:
1. Fahrenheit to Celsius Conversion Formula: The general formula to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C) is:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
This formula is used to find the equivalent temperature in degrees Celsius given the temperature in degrees Fahrenheit.
2. Understanding [tex]$C(F)$[/tex]:
- Here, [tex]$C(F)$[/tex] is a function notation where [tex]$C$[/tex] represents the output in degrees Celsius.
- When you substitute a value of [tex]$F$[/tex] (temperature in Fahrenheit) into this function, it converts that Fahrenheit temperature into Celsius.
3. Interpreting the Function:
- [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex], which is in degrees Celsius.
- The input to the function is [tex]$F$[/tex], which is in degrees Fahrenheit.
Thus, the correct interpretation is 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.
Therefore, the first option is correct:
- [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.