The inverse function is [tex]f^{-1} (x)[/tex]=(x+3)/9.
The given function is f(x)=9x-3.
How to find the inverse of a function?
Steps for finding the inverse of a function f(x).
- Replace f(x) with y in the equation describing the function.
- Interchange x and y. In other words, replace every x with a y and vice versa.
- Solve for y.
- Replace y with [tex]f^{-1} (x)[/tex].
Now, y=9x-3
Interchange x and y. That is x=9y-3.
Solve for y.
That is, 9y=x+3
⇒y=(x+3)/9
⇒[tex]f^{-1} (x)[/tex]=(x+3)/9
Therefore, the inverse function is [tex]f^{-1} (x)[/tex]=(x+3)/9.
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