Answer :
Certainly! Let's go through the question step-by-step to understand what [tex]\( C(F) \)[/tex] represents.
1. Understanding the function:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is the formula used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Breaking it down:
- [tex]\( C(F) \)[/tex]: This notation suggests that [tex]\( C \)[/tex] is a function of [tex]\( F \)[/tex]. This means that [tex]\( C \)[/tex] depends on the value of [tex]\( F \)[/tex].
- What [tex]\( C(F) \)[/tex] represents: When you input a temperature in degrees Fahrenheit (denoted as [tex]\( F \)[/tex]) into the function [tex]\( C \)[/tex], it outputs a value in degrees Celsius. In essence, [tex]\( C(F) \)[/tex] is the temperature in Celsius when you provide a certain Fahrenheit temperature.
3. Clarifying the options:
- Option 1: "[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" is correct. This is because the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] directly translates an input Fahrenheit temperature (F) to an output Celsius temperature.
Thus, [tex]\( C(F) \)[/tex] indeed represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input is in degrees Fahrenheit. This is the correct interpretation of the given function.
1. Understanding the function:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is the formula used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Breaking it down:
- [tex]\( C(F) \)[/tex]: This notation suggests that [tex]\( C \)[/tex] is a function of [tex]\( F \)[/tex]. This means that [tex]\( C \)[/tex] depends on the value of [tex]\( F \)[/tex].
- What [tex]\( C(F) \)[/tex] represents: When you input a temperature in degrees Fahrenheit (denoted as [tex]\( F \)[/tex]) into the function [tex]\( C \)[/tex], it outputs a value in degrees Celsius. In essence, [tex]\( C(F) \)[/tex] is the temperature in Celsius when you provide a certain Fahrenheit temperature.
3. Clarifying the options:
- Option 1: "[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" is correct. This is because the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] directly translates an input Fahrenheit temperature (F) to an output Celsius temperature.
Thus, [tex]\( C(F) \)[/tex] indeed represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input is in degrees Fahrenheit. This is the correct interpretation of the given function.