If f(x)=5x-12, find a value for $x$ so that $f^{-1}(x)=f(x-1)$.
f(x - 1) = 5(x - 1) -12 = 5x - 17
Find the inverse
y = 5x -12
y + 12 = 5x
(y + 12) / 5 = x "swap" x and y
(x + 12) / 5 = y = the inverse
So
(x + 12) / 5 = 5x + 17
x + 12 = 5 ( 5x + 17)
x + 12 = 25x + 85
x - 25x = 85 -12
-24x = 73
x = -73 / 24
