Question

The formula C − 5 sF 2 32d, where F > 2459.67, 9 expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

Answer 1

Answer:

a) The inverse of the function is $F=\frac{9}{5}C+32$

b) The domain of the inverse function is C>1348.70.

Step-by-step explanation:

Given : The formula $C=\frac{5}{9}(F-32)$, where $F>2459.67$ express the Celsius temperature C as a function of the Fahrenheit temperature F.

To find : a) A formula for the inverse function and interpret it.

b) What is the domain of the inverse function?

Solution :

a) The formula $C=\frac{5}{9}(F-32)$

The inverse function of the given formula is the value of F.

Taking F to one side and rest term to other side,

$\frac{9}{5}C=(F-32)$

$\frac{9}{5}C+32=F$

Therefore, The inverse of the function is $F=\frac{9}{5}C+32$

i.e. Fahrenheit temperature F as a function of the Celsius temperature C.

b) The domain of the inverse function.

We have given, $F>2459.67$

Substituting in the formula,

$C=\frac{5}{9}(F-32)$

$C=\frac{5}{9}(2459.67-32)$

$C=\frac{5}{9}(2427.67)$

$C=1348.70$

The domain of the inverse function is C>1348.70.