Respuesta :
Answer:
The required formula for the inverse function is [tex]F=\frac{9C}{5}+32[/tex]
The domain of the inverse function is [tex][-273.15,\infty][/tex]
Step-by-step explanation:
Given : The formula [tex]C=\frac{5}{9}(F-32)[/tex], where [tex]F\geq-459.67[/tex] expresses the Celsius temperature C as a function of the Fahrenheit temperature F.
To find : A formula for the inverse function and What is the domain of the inverse function?
Solution :
a) To find inverse,
The formula is given by,
[tex]C=\frac{5}{9}(F-32)[/tex]
Write the function F in terms of C,
[tex]\frac{9C}{5}=F-32[/tex]
[tex]\frac{9C}{5}+32=F[/tex]
The required formula for the inverse function is
[tex]F=\frac{9C}{5}+32[/tex]
b) To find domain of inverse function,
We have given, [tex]F\geq-459.67[/tex]
So, The domain of the given function is [tex][-459.67,\infty][/tex]
Now, substitute F=-459.67 in the given function to get the domain of the inverse function.
[tex]C=\frac{5}{9}(-459.67-32)[/tex]
[tex]C=\frac{5}{9}(-491.67)[/tex]
[tex]C=-273.15[/tex]
Therefore, the domain of the inverse function is [tex][-273.15,\infty][/tex]
