If _______ , what is f^-1(x)?
f–1(x) = 9x + 18
________
f–1(x) = 9x + 2
________



we have
[tex]f(x)=\frac{1}{9}x-2[/tex]
Let
[tex]y=f(x)[/tex]
[tex]y=\frac{1}{9}x-2[/tex]
To find the inverse
Exchanges the variables x for y and y for x
[tex]x=\frac{1}{9}y-2[/tex]
Isolate the variable y
Multiply by [tex]9[/tex] both sides
[tex]9x=y-18[/tex]
Adds [tex]18[/tex] both sides
[tex]9x+18=y-18+18[/tex]
[tex]y=9x+18[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=9x+18[/tex] -------> the inverse function
therefore
the answer is
[tex]f^{-1}(x)=9x+18[/tex]