Explanation
We must find the inverse function of the line given by:
[tex]y=f(x)=6x+4.[/tex]
(1) First, we find the value of x in terms of y:
[tex]\begin{gathered} y=6x+4, \\ 6x=y-4, \\ x=\frac{y-4}{6}. \end{gathered}[/tex]
(2) We interchange the variables x and y:
[tex]y=\frac{x-4}{6}.[/tex]
The equation obtained is the inverse of f(x):
[tex]f^{-1}(x)=\frac{x-4}{6}.[/tex]Answer
D.
[tex]f^{-1}(x)=\frac{x-4}{6}.[/tex]
