Answer :
Sure! Let's go through the problem step-by-step to understand what the function [tex]\( C(F) \)[/tex] represents:
1. Understanding the Function:
The given function to convert temperatures from Fahrenheit to Celsius is:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
2. Breaking Down the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The term [tex]\( (F - 32) \)[/tex] accounts for the offset between Fahrenheit and Celsius temperature scales.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] converts the adjusted Fahrenheit temperature to degrees Celsius.
3. Interpreting [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] is the result of converting a temperature from Fahrenheit to Celsius using the formula.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius that corresponds to a given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Example Calculation:
Let's verify the conversion with an example:
- If [tex]\( F = 32 \)[/tex] degrees Fahrenheit (freezing point of water), we substitute [tex]\( F \)[/tex] into the function:
[tex]\[
C(32) = \frac{5}{9}(32 - 32) = \frac{5}{9} \times 0 = 0 \text{ degrees Celsius}
\][/tex]
- This tells us that 32 degrees Fahrenheit is equal to 0 degrees Celsius.
Given this analysis, we can deduce the meaning of [tex]\( C(F) \)[/tex] from the options provided:
- The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius
- The temperature of [tex]\( F \)[/tex] degrees Celsius converted to degrees Fahrenheit
- The temperature of [tex]\( C \)[/tex] degrees Fahrenheit converted to degrees Celsius
- The temperature of [tex]\( C \)[/tex] degrees Celsius converted to degrees Fahrenheit
The correct interpretation is:
[tex]\[
\boxed{\text{the temperature of } F \text{ degrees Fahrenheit converted to degrees Celsius}}
\][/tex]
So, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius that is equivalent to a given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
1. Understanding the Function:
The given function to convert temperatures from Fahrenheit to Celsius is:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
2. Breaking Down the Function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The term [tex]\( (F - 32) \)[/tex] accounts for the offset between Fahrenheit and Celsius temperature scales.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] converts the adjusted Fahrenheit temperature to degrees Celsius.
3. Interpreting [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] is the result of converting a temperature from Fahrenheit to Celsius using the formula.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius that corresponds to a given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Example Calculation:
Let's verify the conversion with an example:
- If [tex]\( F = 32 \)[/tex] degrees Fahrenheit (freezing point of water), we substitute [tex]\( F \)[/tex] into the function:
[tex]\[
C(32) = \frac{5}{9}(32 - 32) = \frac{5}{9} \times 0 = 0 \text{ degrees Celsius}
\][/tex]
- This tells us that 32 degrees Fahrenheit is equal to 0 degrees Celsius.
Given this analysis, we can deduce the meaning of [tex]\( C(F) \)[/tex] from the options provided:
- The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius
- The temperature of [tex]\( F \)[/tex] degrees Celsius converted to degrees Fahrenheit
- The temperature of [tex]\( C \)[/tex] degrees Fahrenheit converted to degrees Celsius
- The temperature of [tex]\( C \)[/tex] degrees Celsius converted to degrees Fahrenheit
The correct interpretation is:
[tex]\[
\boxed{\text{the temperature of } F \text{ degrees Fahrenheit converted to degrees Celsius}}
\][/tex]
So, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius that is equivalent to a given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.