Answer:
[tex]f^{-1}(C)=\frac{5}{9}(C-32)[/tex]
Step-by-step explanation:
Given : Function [tex]F(C)=\frac{9}{5}C+32[/tex]
We have to find the inverse of the give function.
Inverse is calculated by putting function f (x) = y ,now taking inverse of f both side , we have, [tex]f^{-1}(y)=x[/tex] and then finding value of x in terms of x. We obtain inverse of function.
Let [tex]F(C)=\frac{9}{5}C+32[/tex]
Put F(C) = y ,
then [tex]f^{-1}(y)=C[/tex] ...........(1)
[tex]y=\frac{9}{5}C+32[/tex]
Subtract 32 both sides, we have,
[tex]y-32=\frac{9}{5}C[/tex]
Now multiply both side by [tex]\frac{5}{9}[/tex] , we have,
[tex]\frac{5}{9}(y-32)=C[/tex] ......(2)
From (1) and (2) , we have,
[tex]f^{-1}(y)=\frac{5}{9}(y-32)[/tex]
Replace y by C, we have,
[tex]f^{-1}(C)=\frac{5}{9}(C-32)[/tex]
