Answer :
To solve this problem, we need to understand what the function [tex]\(C(F) = \frac{5}{9}(F-32)\)[/tex] represents. This formula is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Let's break down the options to identify which one correctly describes what [tex]\(C(F)\)[/tex] does:
1. The temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius:
- This option means that [tex]\(C(F)\)[/tex] takes a temperature in Fahrenheit (represented by [tex]\(F\)[/tex]) and converts it into Celsius. When you plug in a Fahrenheit value into the function [tex]\(C(F)\)[/tex], it performs the necessary computation to give you the Celsius equivalent.
2. The temperature of [tex]\(F\)[/tex] degrees Celsius converted to degrees Fahrenheit:
- This option describes a conversion from Celsius to Fahrenheit. However, the given function [tex]\(C(F) = \frac{5}{9}(F-32)\)[/tex] is designed for the opposite conversion, from Fahrenheit to Celsius.
3. The temperature of [tex]\(C\)[/tex] degrees Fahrenheit converted to degrees Celsius:
- This option wrongly suggests that [tex]\(C\)[/tex] is the input in Fahrenheit. However, [tex]\(C(F)\)[/tex] signifies that [tex]\(F\)[/tex] is the input temperature in Fahrenheit, not [tex]\(C\)[/tex].
4. The temperature of [tex]\(C\)[/tex] degrees Celsius converted to degrees Fahrenheit:
- This is incorrect because it again implies a conversion that the function [tex]\(C(F)\)[/tex] does not perform. The function is for converting Fahrenheit (not Celsius) to Celsius.
After evaluating each option:
- The correct interpretation is that [tex]\(C(F)\)[/tex] represents the temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius.
Therefore, the correct choice is the first option: "the temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius."
Let's break down the options to identify which one correctly describes what [tex]\(C(F)\)[/tex] does:
1. The temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius:
- This option means that [tex]\(C(F)\)[/tex] takes a temperature in Fahrenheit (represented by [tex]\(F\)[/tex]) and converts it into Celsius. When you plug in a Fahrenheit value into the function [tex]\(C(F)\)[/tex], it performs the necessary computation to give you the Celsius equivalent.
2. The temperature of [tex]\(F\)[/tex] degrees Celsius converted to degrees Fahrenheit:
- This option describes a conversion from Celsius to Fahrenheit. However, the given function [tex]\(C(F) = \frac{5}{9}(F-32)\)[/tex] is designed for the opposite conversion, from Fahrenheit to Celsius.
3. The temperature of [tex]\(C\)[/tex] degrees Fahrenheit converted to degrees Celsius:
- This option wrongly suggests that [tex]\(C\)[/tex] is the input in Fahrenheit. However, [tex]\(C(F)\)[/tex] signifies that [tex]\(F\)[/tex] is the input temperature in Fahrenheit, not [tex]\(C\)[/tex].
4. The temperature of [tex]\(C\)[/tex] degrees Celsius converted to degrees Fahrenheit:
- This is incorrect because it again implies a conversion that the function [tex]\(C(F)\)[/tex] does not perform. The function is for converting Fahrenheit (not Celsius) to Celsius.
After evaluating each option:
- The correct interpretation is that [tex]\(C(F)\)[/tex] represents the temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius.
Therefore, the correct choice is the first option: "the temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius."