Answer :
To tackle this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing. Let's break it down step by step:
1. Identify the function: The function provided is [tex]\( C(F) \)[/tex]. Here, [tex]\( C \)[/tex] represents Celsius, and [tex]\( F \)[/tex] represents Fahrenheit. This means that this function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Understand the components:
- The formula starts by taking the input [tex]\( F \)[/tex], which is the temperature in degrees Fahrenheit, and subtracting 32 from it. This is because the Fahrenheit scale's zero point is 32 degrees above the Celsius zero point.
- The result is then multiplied by [tex]\( \frac{5}{9} \)[/tex]. This fraction is the conversion factor between the Fahrenheit and Celsius scales, relating how the increments differ between the two scales.
3. Determine the output: The output of the function, [tex]\( C(F) \)[/tex], is the result of this calculation, which is the temperature value converted into degrees Celsius.
4. Translate the function's purpose:
- [tex]\( C(F) \)[/tex] stands for the temperature in degrees Celsius, which is computed by applying the conversion formula to a temperature originally measured in degrees Fahrenheit.
So, the correct interpretation of what [tex]\( C(F) \)[/tex] represents 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 with the concept that we're converting Fahrenheit temperatures to Celsius using this specific formula.
1. Identify the function: The function provided is [tex]\( C(F) \)[/tex]. Here, [tex]\( C \)[/tex] represents Celsius, and [tex]\( F \)[/tex] represents Fahrenheit. This means that this function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Understand the components:
- The formula starts by taking the input [tex]\( F \)[/tex], which is the temperature in degrees Fahrenheit, and subtracting 32 from it. This is because the Fahrenheit scale's zero point is 32 degrees above the Celsius zero point.
- The result is then multiplied by [tex]\( \frac{5}{9} \)[/tex]. This fraction is the conversion factor between the Fahrenheit and Celsius scales, relating how the increments differ between the two scales.
3. Determine the output: The output of the function, [tex]\( C(F) \)[/tex], is the result of this calculation, which is the temperature value converted into degrees Celsius.
4. Translate the function's purpose:
- [tex]\( C(F) \)[/tex] stands for the temperature in degrees Celsius, which is computed by applying the conversion formula to a temperature originally measured in degrees Fahrenheit.
So, the correct interpretation of what [tex]\( C(F) \)[/tex] represents 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 with the concept that we're converting Fahrenheit temperatures to Celsius using this specific formula.