Answer :
To determine what [tex]$C(F)$[/tex] represents, let's break down the given function:
The function provided is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
This function is used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C). Here's a step-by-step explanation:
1. Understanding Function Notation:
- The function is named [tex]\( C \)[/tex], which suggests it outputs a temperature in degrees Celsius.
- The input variable is [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
2. Function Explanation:
- The function takes an input [tex]\( F \)[/tex], which is a temperature in Fahrenheit, then it performs the calculation [tex]\( \frac{5}{9}(F - 32) \)[/tex] to convert this temperature to Celsius.
3. Calculating the Conversion:
- The formula itself, [tex]\( \frac{5}{9}(F - 32) \)[/tex], is the standard equation used to convert Fahrenheit to Celsius.
- This equation first subtracts 32 from the Fahrenheit temperature because this aligns the freezing points of water in both scales.
- Then, multiplying by [tex]\( \frac{5}{9} \)[/tex], adjusts the scale from Fahrenheit to Celsius.
4. Interpreting the Output:
- The result of this function, [tex]\( C(F) \)[/tex], is thus a temperature value in degrees Celsius.
Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] is:
[tex]\[ C(F) \text{ represents the output of the function } C \text{ in degrees Celsius when the input } F \text{ is in degrees Fahrenheit.} \][/tex]
This corresponds to the first option:
- C(F) represents the output of the function [tex]$C$[/tex] in degrees Celsius when the input [tex]$F$[/tex] is in degrees Fahrenheit.
The function provided is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
This function is used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C). Here's a step-by-step explanation:
1. Understanding Function Notation:
- The function is named [tex]\( C \)[/tex], which suggests it outputs a temperature in degrees Celsius.
- The input variable is [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
2. Function Explanation:
- The function takes an input [tex]\( F \)[/tex], which is a temperature in Fahrenheit, then it performs the calculation [tex]\( \frac{5}{9}(F - 32) \)[/tex] to convert this temperature to Celsius.
3. Calculating the Conversion:
- The formula itself, [tex]\( \frac{5}{9}(F - 32) \)[/tex], is the standard equation used to convert Fahrenheit to Celsius.
- This equation first subtracts 32 from the Fahrenheit temperature because this aligns the freezing points of water in both scales.
- Then, multiplying by [tex]\( \frac{5}{9} \)[/tex], adjusts the scale from Fahrenheit to Celsius.
4. Interpreting the Output:
- The result of this function, [tex]\( C(F) \)[/tex], is thus a temperature value in degrees Celsius.
Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] is:
[tex]\[ C(F) \text{ represents the output of the function } C \text{ in degrees Celsius when the input } F \text{ is in degrees Fahrenheit.} \][/tex]
This corresponds to the first option:
- C(F) represents the output of the function [tex]$C$[/tex] in degrees Celsius when the input [tex]$F$[/tex] is in degrees Fahrenheit.