Answer :
To solve the question about what [tex]$C(F)$[/tex] represents, we need to understand what the notation [tex]$C(F)$[/tex] typically means in a mathematical context. The function [tex]$C(F)$[/tex] is commonly used to express a relationship between two variables and a particular transformation or conversion process. Here's a step-by-step explanation:
1. Identify the Variables:
- [tex]$C$[/tex] generally stands for degrees Celsius.
- [tex]$F$[/tex] generally stands for degrees Fahrenheit.
2. Understand Function Notation:
- [tex]$C(F)$[/tex] indicates that we have a function named [tex]$C$[/tex] where the input variable is [tex]$F$[/tex].
- In terms of functions, this notation signifies how we convert input values (in Fahrenheit) to output values (in Celsius).
3. Interpret the Possible Answers:
- 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.
- This option indicates that we're converting from Fahrenheit to Celsius, which is a common conversion task.
- Option 2: [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Fahrenheit when the input [tex]$C$[/tex] is in degrees Celsius.
- This is incorrect because it reverses the roles of [tex]$C$[/tex] and [tex]$F$[/tex].
- Option 3: [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex] in degrees Fahrenheit when the input [tex]$F$[/tex] is in degrees Celsius.
- This is also incorrect because it suggests the input is in Celsius, which contradicts the way the function is usually defined.
- Option 4: [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Celsius when the input [tex]$C$[/tex] is in degrees Fahrenheit.
- This is incorrect due to the mislabeling of input and output.
4. Choose the Correct Interpretation:
- The correct option describes a function [tex]$C(F)$[/tex] that converts from an input in Fahrenheit to an output in Celsius, which aligns with how temperatures are typically converted between these two scales.
Hence, the correct interpretation is:
[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 is consistent with the conventional use of a function that converts temperature from Fahrenheit to Celsius.
1. Identify the Variables:
- [tex]$C$[/tex] generally stands for degrees Celsius.
- [tex]$F$[/tex] generally stands for degrees Fahrenheit.
2. Understand Function Notation:
- [tex]$C(F)$[/tex] indicates that we have a function named [tex]$C$[/tex] where the input variable is [tex]$F$[/tex].
- In terms of functions, this notation signifies how we convert input values (in Fahrenheit) to output values (in Celsius).
3. Interpret the Possible Answers:
- 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.
- This option indicates that we're converting from Fahrenheit to Celsius, which is a common conversion task.
- Option 2: [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Fahrenheit when the input [tex]$C$[/tex] is in degrees Celsius.
- This is incorrect because it reverses the roles of [tex]$C$[/tex] and [tex]$F$[/tex].
- Option 3: [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex] in degrees Fahrenheit when the input [tex]$F$[/tex] is in degrees Celsius.
- This is also incorrect because it suggests the input is in Celsius, which contradicts the way the function is usually defined.
- Option 4: [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Celsius when the input [tex]$C$[/tex] is in degrees Fahrenheit.
- This is incorrect due to the mislabeling of input and output.
4. Choose the Correct Interpretation:
- The correct option describes a function [tex]$C(F)$[/tex] that converts from an input in Fahrenheit to an output in Celsius, which aligns with how temperatures are typically converted between these two scales.
Hence, the correct interpretation is:
[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 is consistent with the conventional use of a function that converts temperature from Fahrenheit to Celsius.
