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

a) The inverse of the function is
`F=(9)/(5)C+32`

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

Explanation:

Given : The formula
`C=(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=(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,

`(9)/(5)C=(F-32)`

`(9)/(5)C+32=F`

Therefore, The inverse of the function is
`F=(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=(5)/(9)(F-32)`

`C=(5)/(9)(2459.67-32)`

`C=(5)/(9)(2427.67)`

`C=1348.70`

The domain of the inverse function is C>1348.70.