Answer :
To understand what [tex]\( C(F) \)[/tex] represents, let's look at the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is a formula used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Let's break it down:
1. Input: The function uses [tex]\( F \)[/tex], which is the temperature in degrees Fahrenheit, as the input.
2. Calculation: The function subtracts 32 from [tex]\( F \)[/tex]. This is because the starting point for the conversion is 32 degrees Fahrenheit, which equals 0 degrees Celsius.
3. The result, [tex]\( (F - 32) \)[/tex], is then multiplied by [tex]\( \frac{5}{9} \)[/tex]. This fraction is used to scale the temperature difference appropriately between Fahrenheit and Celsius scales.
4. Output: The output of this function, [tex]\( C(F) \)[/tex], is the corresponding temperature in degrees Celsius.
Therefore, [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is given in degrees Fahrenheit. This makes the correct answer:
"[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."
Let's break it down:
1. Input: The function uses [tex]\( F \)[/tex], which is the temperature in degrees Fahrenheit, as the input.
2. Calculation: The function subtracts 32 from [tex]\( F \)[/tex]. This is because the starting point for the conversion is 32 degrees Fahrenheit, which equals 0 degrees Celsius.
3. The result, [tex]\( (F - 32) \)[/tex], is then multiplied by [tex]\( \frac{5}{9} \)[/tex]. This fraction is used to scale the temperature difference appropriately between Fahrenheit and Celsius scales.
4. Output: The output of this function, [tex]\( C(F) \)[/tex], is the corresponding temperature in degrees Celsius.
Therefore, [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is given in degrees Fahrenheit. This makes the correct answer:
"[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."