ANSWER
F⁻¹(x) = 6(x - 3)
EXPLANATION
To find the inverse function we have to clear x as a function of f. In this function
[tex]F(x)=\frac{x}{6}+3[/tex]
the first step is to subtract 3 from both sides of the equation:
[tex]\begin{gathered} F(x)-3=\frac{x}{6}+3-3 \\ F(x)-3=\frac{x}{6} \end{gathered}[/tex]
And then multiply both sides by 6:
[tex]\begin{gathered} 6(F(x)-3)=\frac{x}{6}\cdot6 \\ 6(F(x)-3)=x \end{gathered}[/tex]
Finally change the names of x and F(x). x is now F⁻¹(x) and F(x) is now x:
[tex]F^{-1}(x)=6(x-3)[/tex]
