Question

Function F, shown below, assigns to a temperature given in degrees Celsius its equivalent in degrees Fahrenheit. Function C, also shown below, assigns to a temperature given in degrees Kelvin its equivalent in degrees Celsius. Choose the response below the shows the correct expression for F(C(x)) and then choose the response below that correctly interprets the meaning of F(C(x)).

Answer 1

$\begin{gathered} F(x)=\frac{9}{5}x+32 \\ \\ C(x)=x-273 \end{gathered}$

Find F(C(x)): Write F and substitute the x by C(x):

$\begin{gathered} F(C(x))=\frac{9}{5}(C(x))+32 \\ \\ F(C(x))=\frac{9}{5}(x-273)+32 \\ \\ F(C(x))=\frac{9}{5}x-\frac{2457}{5}+32 \\ \\ F(C(x))=\frac{9}{5}x-\frac{2457}{5}+\frac{160}{5} \\ \\ F(C(x))=\frac{9}{5}x-\frac{2297}{5} \\ \\ F(C(x))=\frac{9}{5}x-459\frac{2}{5} \end{gathered}$

As you write F in terms of C it means that F(C(x)) take a temperature given in degrees Kelvin and converts it to degrees Farenheit.

Answers:

$F(C(x))=(\frac{9}{5})x-459\frac{2}{5}$

F(C(x)) take a temperature given in degrees Kelvin and converts it to degrees Farenheit