Answer :
Certainly! Let's go through the question step-by-step to understand what [tex]$C(F)$[/tex] represents when converting temperatures from Fahrenheit to Celsius.
1. Understand the Symbols:
- [tex]$C(F)$[/tex] is a function that takes an input [tex]$F$[/tex].
- [tex]$F$[/tex] represents a temperature in degrees Fahrenheit.
- [tex]$C(F)$[/tex] will give us the equivalent temperature in degrees Celsius.
2. Look at the Formula:
- The function provided is [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex].
- This is a standard formula for converting Fahrenheit temperatures to Celsius.
3. Interpreting the Function:
- When you input a temperature in degrees Fahrenheit ([tex]$F$[/tex]), the formula [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex] calculates the corresponding temperature in degrees Celsius.
- The operation [tex]$(F - 32)$[/tex] accounts for the difference between the freezing point of water in Fahrenheit (32°F) and Celsius (0°C).
- Multiplying by [tex]$\frac{5}{9}$[/tex] adjusts for the difference in scale between Fahrenheit and Celsius degrees.
4. Conclusion:
- [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] gives you the converted Celsius temperature corresponding to the given Fahrenheit temperature.
So, the correct interpretation is that [tex]$C(F)$[/tex] gives the temperature in Celsius for a given temperature in Fahrenheit.
1. Understand the Symbols:
- [tex]$C(F)$[/tex] is a function that takes an input [tex]$F$[/tex].
- [tex]$F$[/tex] represents a temperature in degrees Fahrenheit.
- [tex]$C(F)$[/tex] will give us the equivalent temperature in degrees Celsius.
2. Look at the Formula:
- The function provided is [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex].
- This is a standard formula for converting Fahrenheit temperatures to Celsius.
3. Interpreting the Function:
- When you input a temperature in degrees Fahrenheit ([tex]$F$[/tex]), the formula [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex] calculates the corresponding temperature in degrees Celsius.
- The operation [tex]$(F - 32)$[/tex] accounts for the difference between the freezing point of water in Fahrenheit (32°F) and Celsius (0°C).
- Multiplying by [tex]$\frac{5}{9}$[/tex] adjusts for the difference in scale between Fahrenheit and Celsius degrees.
4. Conclusion:
- [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] gives you the converted Celsius temperature corresponding to the given Fahrenheit temperature.
So, the correct interpretation is that [tex]$C(F)$[/tex] gives the temperature in Celsius for a given temperature in Fahrenheit.