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12345 [234]
3 years ago
10

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

Mathematics
2 answers:
castortr0y [4]3 years ago
8 0

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

In-s [12.5K]3 years ago
3 0

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)    

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