To convert temperatures from degrees Celsius to degrees Fahrenheit, you can use the function F(x)=9/5x+32 where x is the temperature in degrees Celsius. To convert temperatures from degrees Kelvin to degrees Celsius, you can use the function C(x)=x-273.15, where x is the temperature in degrees Kelvin. Find the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit.
(C * F)(x)=9/5x - 241.15
(F * C)(x)=9/5x - 241.15
(C * F)(x)=9/5(x-273.15)+32
(F * C)(x)=9/5(x-273.15)+32
Function wise, I know that it's either the third or fourth option, I just don't know if it's (C*F) or (F*C). Please help? Thanks
starting with Kelvin and going to Fahrenheit
Kelvin feeds into C(x)
C(x) feeds into F(x)
sometimes written as ... F(C(x))
F of C of x
Okay, thanks Scott:)
To find the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit, we need to evaluate the composition of the two given functions.
The first function is F(x) = 9/5x + 32, which converts temperatures from degrees Celsius to degrees Fahrenheit.
The second function is C(x) = x - 273.15, which converts temperatures from degrees Kelvin to degrees Celsius.
To convert temperatures from degrees Kelvin to degrees Fahrenheit, we can perform the composition of these two functions, which means applying the Celsius-to-Fahrenheit conversion after converting Kelvin to Celsius.
Let's calculate this composite function:
(F * C)(x) = F(C(x))
= F(x - 273.15)
= (9/5)(x - 273.15) + 32
= (9/5)x - 491.67 + 32
= (9/5)x - 459.67
Therefore, the correct composite function to convert temperatures from degrees Kelvin to degrees Fahrenheit is: (F * C)(x) = (9/5)x - 459.67.
To determine the correct order of the composite function that converts temperatures from degrees Kelvin to degrees Fahrenheit, we need to consider the order in which the temperature conversions should occur.
The composite function notation (C * F)(x) represents first applying the function C(x) to the input x, and then taking the result and applying the function F to it.
Let's analyze the options:
1. (C * F)(x) = 9/5x - 241.15: This option represents applying the function F(x) (converting from Celsius to Fahrenheit) first and then applying the function C(x) (converting from Kelvin to Celsius). This order is incorrect because converting from Kelvin to Celsius should be done before converting to Fahrenheit.
2. (F * C)(x) = 9/5x - 241.15: This option represents applying the function C(x) (converting from Kelvin to Celsius) first, and then applying the function F(x) (converting from Celsius to Fahrenheit). This order is incorrect as well because we need to convert to Celsius before converting to Fahrenheit.
3. (C * F)(x) = 9/5(x-273.15)+32: This option represents first applying the function F(x) (converting from Celsius to Fahrenheit) and then applying the function C(x) (converting from Kelvin to Celsius). This order is incorrect because converting from Kelvin to Celsius should be done first.
4. (F * C)(x) = 9/5(x-273.15)+32: This option represents applying the function C(x) (converting from Kelvin to Celsius) first, and then applying the function F(x) (converting from Celsius to Fahrenheit). This order is correct because converting from Kelvin to Celsius should be done first, and then Celsius to Fahrenheit.
Therefore, the correct composite function to convert temperatures from degrees Kelvin to degrees Fahrenheit is (F * C)(x) = 9/5(x-273.15)+32.