Answer :
To solve this question, we need to understand what the function [tex]\(C(F) = \frac{5}{9}(F - 32)\)[/tex] does. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Here's a breakdown of the process:
1. Identify the Components of the Function:
- The input to the function is [tex]\(F\)[/tex], which represents a temperature in degrees Fahrenheit.
- The formula [tex]\(\frac{5}{9}(F - 32)\)[/tex] converts that temperature into degrees Celsius.
2. Understanding the Conversion:
- The conversion formula is a standard one used to change temperatures from Fahrenheit to Celsius. It subtracts 32 from the Fahrenheit temperature and then multiplies by [tex]\(\frac{5}{9}\)[/tex].
3. Determine What [tex]\(C(F)\)[/tex] Represents:
- Since [tex]\(C(F)\)[/tex] is the result of applying the function to a Fahrenheit temperature [tex]\(F\)[/tex], it gives us the equivalent temperature in degrees Celsius.
Given these points, the correct interpretation of [tex]\(C(F)\)[/tex] in context with the options provided is:
- [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 matches the first option provided in the question.
Here's a breakdown of the process:
1. Identify the Components of the Function:
- The input to the function is [tex]\(F\)[/tex], which represents a temperature in degrees Fahrenheit.
- The formula [tex]\(\frac{5}{9}(F - 32)\)[/tex] converts that temperature into degrees Celsius.
2. Understanding the Conversion:
- The conversion formula is a standard one used to change temperatures from Fahrenheit to Celsius. It subtracts 32 from the Fahrenheit temperature and then multiplies by [tex]\(\frac{5}{9}\)[/tex].
3. Determine What [tex]\(C(F)\)[/tex] Represents:
- Since [tex]\(C(F)\)[/tex] is the result of applying the function to a Fahrenheit temperature [tex]\(F\)[/tex], it gives us the equivalent temperature in degrees Celsius.
Given these points, the correct interpretation of [tex]\(C(F)\)[/tex] in context with the options provided is:
- [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 matches the first option provided in the question.