Call f(x) = y
y = x / 4 - 2 Interchange x and y
x = y/4 - 2 Add 2 to both sides.
(x + 2) = y/4 Multiply by 4
4(x + 2) = y This is a new y which the question has labeled as r-1(x)
4(x + 2) = r-1(x)
Answer D <<<<< answer.
It is very instructive to plot both these graphs. See below. When you do and you add y = x, the two graphs, the original and the inverse reflect around y = x. Every inverse does this.
y = x/4 - 2 red
r-1(x) = 4(x + 2) blue
y = x green.
Answer D <<<<<