Given:
The function is
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]
Required:
Find the inverse of the function.
Explanation:
The given function is:
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]
Put
[tex]f(x)=y[/tex][tex]y=\frac{\sqrt{x-2}}{6}[/tex]
Interchange x and y.
[tex]x=\frac{\sqrt{y-2}}{6}[/tex]
Take the square on both sides.
[tex]x^2=\frac{y-2}{36}[/tex][tex]\begin{gathered} 36x^2=y-2 \\ y=36x^2+2 \end{gathered}[/tex]
Substitute
[tex]y=f^{-1}(x)[/tex][tex]f^{-1}(x)=36x^2+2[/tex]
Final Answer:
Option A is the correct answer.
