Answer :
To solve the problem of understanding what [tex]$C(F)$[/tex] represents in the given context, let's break down the function and the information provided:
1. Understanding the function:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is a mathematical formula used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
2. Analyzing the components of the formula:
- [tex]\( F \)[/tex]: This represents the temperature in degrees Fahrenheit. It is the input for the function.
- [tex]\( C(F) \)[/tex]: This represents the output of the function, which is the temperature in degrees Celsius after the conversion.
3. Checking what the function does:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] takes a Fahrenheit temperature (F) and subtracts 32, then multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This standard conversion process will give you the temperature in degrees Celsius, which is the output.
4. Clarifying the options:
- The correct interpretation here is that [tex]\( C(F) \)[/tex] is meant to provide the temperature in degrees Celsius once you have plugged in the Fahrenheit temperature as the input.
Therefore, based on this breakdown and understanding, the correct statement about what [tex]\( C(F) \)[/tex] represents is:
- "C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
1. Understanding the function:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is a mathematical formula used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
2. Analyzing the components of the formula:
- [tex]\( F \)[/tex]: This represents the temperature in degrees Fahrenheit. It is the input for the function.
- [tex]\( C(F) \)[/tex]: This represents the output of the function, which is the temperature in degrees Celsius after the conversion.
3. Checking what the function does:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] takes a Fahrenheit temperature (F) and subtracts 32, then multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This standard conversion process will give you the temperature in degrees Celsius, which is the output.
4. Clarifying the options:
- The correct interpretation here is that [tex]\( C(F) \)[/tex] is meant to provide the temperature in degrees Celsius once you have plugged in the Fahrenheit temperature as the input.
Therefore, based on this breakdown and understanding, the correct statement about what [tex]\( C(F) \)[/tex] represents is:
- "C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."