To convert a temperature from Kelvin (K) directly to Fahrenheit (F), we need to combine the two given functions:
1. Convert Kelvin (K) to Celsius (C) using the function:
[tex]\[
C(K) = K - 273.15
\][/tex]
2. Convert the result from Celsius (C) to Fahrenheit (F) using the function:
[tex]\[
F(C) = \frac{9}{5} C + 32
\][/tex]
Let's combine these two steps into one function:
1. Substitute the first equation into the second equation. Start by expressing Celsius in terms of Kelvin:
[tex]\[
C = K - 273.15
\][/tex]
2. Now, substitute [tex]\(C = K - 273.15\)[/tex] in the Fahrenheit function [tex]\(F(C) = \frac{9}{5} C + 32\)[/tex]:
[tex]\[
F(K) = \frac{9}{5} (K - 273.15) + 32
\][/tex]
Thus, the correct combined function for converting temperature from Kelvin (K) to Fahrenheit (F) is:
[tex]\[
F(K) = \frac{9}{5} (K - 273.15) + 32
\][/tex]
This corresponds to option [tex]\( \text{D} \)[/tex]:
[tex]\[
D. \frac{9}{5}(K-273.15) + 32
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{4} \)[/tex].
