Respuesta :

altavistard
Please, try typing

  -1
f     (x)  to indicate "inverse function."

Type   f(x) = 1/9x -2    as   f(x) = (1/9)x -2

1) replace f(x) with y:          y =  (1/9)x -2
2)  Interchange x and y:      x = (1/9)y - 2
3)  Solve for y:                     9x = y - 18, or y = 9x + 18
4)  replace y with 

  -1
f     (x)   

Then

   -1 
f      (x) = 9x + 18   (answer)

Answer:

[tex]f^{-1}(x)[/tex] will be equal to 9y+18

Step-by-step explanation:

We have given [tex]f(x)=\frac{1}{9}x-2[/tex]

Now let [tex]f(x)=y[/tex]

So [tex]y=\frac{1}{9}x-2[/tex]

We have to find [tex]f^{-1}(x)[/tex] , means value of x in terms of y

So [tex]y=\frac{1}{9}x-2[/tex]

[tex]y+2=\frac{1}{9}x[/tex]

[tex]x=9y+18[/tex]

So [tex]f^{-1}(x)[/tex] will be equal to 9y+18

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