Respuesta :

notnophyco

f(x)=19x+2→ Switch the f(x) with a y


y=19x+2→ Switch the places of the x and the y variables


x=19y+2→ Solve for y


x−2=19y


y=9x−18


The inverse is f−1(x)=9x−18

Answer:

Option A is correct

[tex]f^{-1}(x) = 9x+18[/tex]    

Step-by-step explanation:

Given the function:

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

Let y = f(x)

then;

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

Replace x and y values we have;

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

Add 2 to both sides we have

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

Multiply both sides by 9, to solve for y

[tex]9(x+2) = y[/tex]

or

y = 9(x+2)

replace [tex]y = f^{-1} (x)[/tex] then;

[tex]f^{-1}(x) = 9(x+2)[/tex]

⇒[tex]f^{-1}(x) = 9x+18[/tex]

therefore, the inverse of f(x) is, [tex]f^{-1}(x) = 9x+18[/tex]

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