Question

The inverse of F(C) = 9 5 C + 32 is

Answer 1

F(C) = 95C + 32...
F(C) is y.
y = 95C + 32
Switch Y & C.
C = 95y + 32
C - 32 = 95y
(C - 32) / 95 = y
In the inverse, y is F-1(C)

F-1(C) = (C - 32) / 95

Answer 2

Answer:

$f^{-1}(C)=\frac{5}{9}(C-32)$  

Step-by-step explanation:

Given : Function $F(C)=\frac{9}{5}C+32$

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, $f^{-1}(y)=x$ and then finding value of x in terms of x. We obtain inverse of function.

Let  $F(C)=\frac{9}{5}C+32$

Put F(C) = y ,

then $f^{-1}(y)=C$  ...........(1)

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

Subtract 32 both sides, we have,

$y-32=\frac{9}{5}C$

Now multiply both side by  $\frac{5}{9}$ , we have,

$\frac{5}{9}(y-32)=C$  ......(2)

From (1) and (2) , we have,

$f^{-1}(y)=\frac{5}{9}(y-32)$  

Replace y by C, we have,

$f^{-1}(C)=\frac{5}{9}(C-32)$