Question

if f(x)=1/9x-2, what is f^-1(x)

Answer 1

You first switch f(x) with x in this equation
\[x = \frac{ 1 }{ 9f(x) - 2 }\]
Then you solve for f(x).
\[9f(x) -2 = \frac{ 1 }{ x }\]
\[9f(x) = \frac{ 1 }{ x } + 2\]
\[f(x) = \frac{ 1 }{ 9x } + \frac{ 2 }{ 9 }\]
Then you simply repalace f(x) with f^-1(x)
It will look like this
\[f^-1(x) = \frac{ 1 }{ 9x } + \frac{ 2 }{ 9 }\]