we have the function
[tex]f(x)=\log _43x+2[/tex]step 1
Let
y=f(x)
[tex]y=\log _43x+2[/tex]step 2
Exchange the variables (x for y and y for x)
[tex]x=\log _43y+2[/tex]step 3
Isolate the variable y
[tex]\begin{gathered} x=\log _43y+2 \\ (x-2)=\log _43y \\ 4^{(x-2)}=3y^{} \\ y=\frac{4^{(x-2)}}{3} \end{gathered}[/tex]therefore
The inverse function is equal to
[tex]f^{-1}(x)=\frac{4^{(x-2)}}{3}[/tex]