Given:
The function is:
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
To find:
The value of [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=\dfrac{1}{9}x-2[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{1}{9}y-2[/tex]
Step 3: Isolate the variable [tex]y[/tex].
[tex]x+2=\dfrac{1}{9}y[/tex]
[tex]9(x+2)=y[/tex]
[tex]9x+18=y[/tex]
[tex]y=9x+18[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=9x+18[/tex]
Therefore, the required function is [tex]f^{-1}(x)=9x+18[/tex].
