Answer :
To solve the question about what [tex]\( C(F) \)[/tex] represents, let's break down the function and examine what each part means:
1. Function Definition: The function is given as [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. Understanding the Function:
- The input to this function is [tex]\( F \)[/tex], which represents temperature in degrees Fahrenheit.
- The output of the function is [tex]\( C(F) \)[/tex], which represents temperature in degrees Celsius.
3. Purpose of the Function:
- The purpose of this function is to take a temperature value in Fahrenheit, apply the conversion formula, and produce the equivalent temperature in Celsius.
4. Analyzing the Choices:
- Choice 1: [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.
- This statement is correct because it accurately describes the function's purpose: converting Fahrenheit to Celsius.
- Choice 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
- This statement is incorrect because it describes an inverse situation that the function is not designed for.
- Choice 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- This statement is incorrect because it reverses the input-output roles and units.
- Choice 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- This statement is incorrect for similarly reversing the roles and misidentifying the units.
Based on this analysis, choice 1 is the correct interpretation of the function [tex]\( C(F) \)[/tex]. Therefore, [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.
1. Function Definition: The function is given as [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. Understanding the Function:
- The input to this function is [tex]\( F \)[/tex], which represents temperature in degrees Fahrenheit.
- The output of the function is [tex]\( C(F) \)[/tex], which represents temperature in degrees Celsius.
3. Purpose of the Function:
- The purpose of this function is to take a temperature value in Fahrenheit, apply the conversion formula, and produce the equivalent temperature in Celsius.
4. Analyzing the Choices:
- Choice 1: [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.
- This statement is correct because it accurately describes the function's purpose: converting Fahrenheit to Celsius.
- Choice 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
- This statement is incorrect because it describes an inverse situation that the function is not designed for.
- Choice 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- This statement is incorrect because it reverses the input-output roles and units.
- Choice 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- This statement is incorrect for similarly reversing the roles and misidentifying the units.
Based on this analysis, choice 1 is the correct interpretation of the function [tex]\( C(F) \)[/tex]. Therefore, [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.