Answer :
To solve this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents. This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Let's break down the function step-by-step:
1. Understand the Components of the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the resulting temperature in degrees Celsius after the conversion.
2. Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert Fahrenheit to Celsius.
- The part [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by subtracting 32, which is necessary because 32 degrees Fahrenheit is the freezing point of water — equivalent to 0 degrees Celsius.
- The multiplication by [tex]\( \frac{5}{9} \)[/tex] scales the adjusted temperature to match the Celsius scale, which progresses at a different rate compared to Fahrenheit.
3. What Does [tex]\( C(F) \)[/tex] Represent?
- [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius that corresponds to [tex]\( F \)[/tex] degrees Fahrenheit.
4. Example to Verify:
- If we take an example where [tex]\( F = 32 \)[/tex] (the freezing point of water), plug it into the conversion formula:
[tex]\[
C(F) = \frac{5}{9}(32 - 32) = \frac{5}{9} \times 0 = 0
\][/tex]
- This calculation shows that 32 degrees Fahrenheit is indeed 0 degrees Celsius, demonstrating the proper conversion.
Therefore, [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
Let's break down the function step-by-step:
1. Understand the Components of the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the resulting temperature in degrees Celsius after the conversion.
2. Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert Fahrenheit to Celsius.
- The part [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by subtracting 32, which is necessary because 32 degrees Fahrenheit is the freezing point of water — equivalent to 0 degrees Celsius.
- The multiplication by [tex]\( \frac{5}{9} \)[/tex] scales the adjusted temperature to match the Celsius scale, which progresses at a different rate compared to Fahrenheit.
3. What Does [tex]\( C(F) \)[/tex] Represent?
- [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius that corresponds to [tex]\( F \)[/tex] degrees Fahrenheit.
4. Example to Verify:
- If we take an example where [tex]\( F = 32 \)[/tex] (the freezing point of water), plug it into the conversion formula:
[tex]\[
C(F) = \frac{5}{9}(32 - 32) = \frac{5}{9} \times 0 = 0
\][/tex]
- This calculation shows that 32 degrees Fahrenheit is indeed 0 degrees Celsius, demonstrating the proper conversion.
Therefore, [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.