Given a function as shown below:
[tex]g(x)\text{ = }\frac{x-2}{5}[/tex][tex]\begin{gathered} g(x)=\frac{x-2}{5} \\ \text{Inverse of g(x) = g}^{-1}(x) \\ \text{cross multiply } \\ \text{5g(x) = x-2} \\ 5g(x)+2\text{ = x} \\ x=5g(x)+2 \end{gathered}[/tex][tex]g^{-1}(x)=5x+2[/tex]Since the function of f(x) = 5x+2 and also inverse of g(x) = 5x+2
Therefore from the observation, the inverse of g(x) is similar to the function of f(x)
Hence the function of f(x) = inverse of g(x)
