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The function [tex]$F(C)=\frac{9}{5} C+32$[/tex] is used to convert temperature from Celsius [tex]$(C)$[/tex] to Fahrenheit [tex]$(F)$[/tex]. The function [tex]$C(K)=K-273.15$[/tex] is used to convert temperature from Kelvin [tex]$(K)$[/tex] to Celsius. Which is the correct function for converting temperature from Kelvin to Fahrenheit?

A. [tex]$\frac{9}{5}(K-273.15)$[/tex]
B. [tex]$\frac{9}{5} C-273.15$[/tex]
C. [tex]$\frac{9}{5} C+32-273.15$[/tex]
D. [tex]$\frac{9}{5}(K-273.15)+32$[/tex]



Answer :

GinnyAnswer
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].

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