To determine the correct function for converting temperature from Kelvin (K) to Fahrenheit (F), we need to combine the two given conversion formulas in a step-by-step process.
1. Convert Kelvin to Celsius:
The formula for converting Kelvin to Celsius is given by:
[tex]\[
C(K) = K - 273.15
\][/tex]
This means that if you have a temperature in Kelvin, you subtract 273.15 to get the equivalent temperature in Celsius.
2. Convert Celsius to Fahrenheit:
The formula for converting Celsius to Fahrenheit is given by:
[tex]\[
F(C) = \frac{9}{5}C + 32
\][/tex]
This means that if you have a temperature in Celsius, you use \(\frac{9}{5}\) times the Celsius temperature and then add 32 to get the equivalent temperature in Fahrenheit.
To find the function that directly converts Kelvin to Fahrenheit, we need to substitute the Celsius conversion into the Fahrenheit conversion.
3. Substitute \(C(K) = K - 273.15\) into \(F(C)\):
[tex]\[
F(K) = \frac{9}{5}(K - 273.15) + 32
\][/tex]
By performing this substitution, we effectively combine both conversion steps into one formula.
Therefore, the correct function for converting temperature from Kelvin to Fahrenheit is:
[tex]\[
F(K) = \frac{9}{5}(K - 273.15) + 32
\][/tex]
Based on the options provided, the correct answer is:
D. \(\frac{9}{8}(K-273.15)+32\)
However, this needs further scrutiny to affirm; checking the simplified coefficients and given constants the final correct form is
[tex]\[
F(K) = \frac{9}{5}(K - 273.15) + 32
\][/tex]
Matching with:
Answer A:\(\frac{9}{5}(K-273.15)+32)>= The simplified form consistent with the conversion process
