Answer :
To understand what [tex]\( C(F) \)[/tex] represents, let's take a closer look at the function given in the problem:
The function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Here’s how it works:
1. Input: The function takes an input [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
2. Calculation:
- First, it subtracts 32 from the input temperature [tex]\( F \)[/tex]. This adjustment is necessary because the Fahrenheit and Celsius scales are offset by 32 degrees at the point where water freezes (32°F = 0°C).
- Next, it multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This is the conversion factor that adjusts the size of the Celsius degree relative to the Fahrenheit degree. This ratio comes from the fact that there are 180 Fahrenheit degrees between freezing and boiling point of water (32°F to 212°F), but only 100 Celsius degrees for the same interval (0°C to 100°C), which simplifies to a ratio of [tex]\(\frac{5}{9}\)[/tex].
3. Output: The function returns [tex]\( C(F) \)[/tex], which is the temperature in degrees Celsius.
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. This means:
[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.
The function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Here’s how it works:
1. Input: The function takes an input [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
2. Calculation:
- First, it subtracts 32 from the input temperature [tex]\( F \)[/tex]. This adjustment is necessary because the Fahrenheit and Celsius scales are offset by 32 degrees at the point where water freezes (32°F = 0°C).
- Next, it multiplies the result by [tex]\(\frac{5}{9}\)[/tex]. This is the conversion factor that adjusts the size of the Celsius degree relative to the Fahrenheit degree. This ratio comes from the fact that there are 180 Fahrenheit degrees between freezing and boiling point of water (32°F to 212°F), but only 100 Celsius degrees for the same interval (0°C to 100°C), which simplifies to a ratio of [tex]\(\frac{5}{9}\)[/tex].
3. Output: The function returns [tex]\( C(F) \)[/tex], which is the temperature in degrees Celsius.
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. This means:
[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.