A) He knows that the temperature in degrees Fahrenheit, $F$, is given by the equation $$F=g(C)=\frac{9}{5}C+32,$$ where $C$ is the temperature in degrees Celsius.

I) Find a formula for $g^{-1}(F)$. What are the units of the inputs and outputs?
$g^{-1}(F)=$
Input units: ? degrees Fahrenheit degrees Celsius
Output units: ? degrees Fahrenheit degrees Celsius

II) Evaluate and interpret $g(33)$ and $g^{-1}(33)$.
$g(33)=$

A. It is the temperature in degrees Fahrenheit when the temperature is 33 degrees Celsius.

B. It is the temperature in degrees Celsius when the temperature is 33 degrees Fahrenheit.

C. It means it's 33 degrees Fahrenheit.

D. It means it's 33 degrees Celsius.


$g^{-1}(33)=$

A. It is the temperature in degrees Fahrenheit when the temperature is 33 degrees Celsius.

B. It is the temperature in degrees Celsius when the temperature is 33 degrees Fahrenheit.

C. It means it's 33 degrees Fahrenheit.

D. It means it's 33 degrees Celsius.

B) Schuyler also always needs to keep the currency exchange rate in mind: $D=f(K)=0.15K$, where $D$ is the value in US dollars, and $K$ is the value in Danish krones.

I) Find a formula for $f^{-1}(D)$, and interpret its meaning in the context of the problem. What are the units of the inputs and outputs?
$f^{-1}(D)=$
Input units: ? US dollars Danish krones
Output units: ? US dollars Danish krones

II) Evaluate and interpret $f(60)$ and $f^{-1}(100)$.
$f(60)=$

A. It is the value of 60 Danish krones in US dollars.

B. It is the value of 60 US dollars in Danish krones.

C. It means Schuyler has 60 US dollars.

D. It means Schuyler has 60 Danish krones.


$f^{-1}(100)=$

A. It is the value of 100 Danish krones in US dollars.

B. It is the value of 100 US dollars in Danish krones.

C. It means Schuyler has 100 US dollars.

D. It means Schuyler has 100 Danish krones.

C) Suppose the monthly cost in Danish krones of heating Schuyler's apartment to $x$ degrees Celsius is given by $H(x)=32x$. Evaluate and interpret $f(H(g^{-1}(70)))$.
$f(H(g^{-1}(70)))=$

A. It is the cost to heat Schuyler's apartment to 70 degrees Fahrenheit in Danish krones.

B. It is the cost to heat Schuyler's apartment to 70 degrees Fahrenheit in US dollars.

C. It is the cost to heat Schuyler's apartment to 70 degrees Celsius in US dollars.

D. It is the cost to heat Schuyler's apartment to 70 degrees Celsius in Danish krones.

Hint: