Respuesta :
Answer:
a) The inverse of the function is [tex]F=\frac{9}{5}C+32[/tex]
b) The domain of the inverse function is C>1348.70.
Step-by-step explanation:
Given : The formula [tex]C=\frac{5}{9}(F-32)[/tex], where [tex]F>2459.67[/tex] 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 [tex]C=\frac{5}{9}(F-32)[/tex]
The inverse function of the given formula is the value of F.
Taking F to one side and rest term to other side,
[tex]\frac{9}{5}C=(F-32)[/tex]
[tex]\frac{9}{5}C+32=F[/tex]
Therefore, The inverse of the function is [tex]F=\frac{9}{5}C+32[/tex]
i.e. Fahrenheit temperature F as a function of the Celsius temperature C.
b) The domain of the inverse function.
We have given, [tex]F>2459.67[/tex]
Substituting in the formula,
[tex]C=\frac{5}{9}(F-32)[/tex]
[tex]C=\frac{5}{9}(2459.67-32)[/tex]
[tex]C=\frac{5}{9}(2427.67)[/tex]
[tex]C=1348.70[/tex]
The domain of the inverse function is C>1348.70.
