Let
f(x) = k(x) if x > 2
f(x) = -3x + 8 if x <= 2
Find the function k(x) such that f(x) is its own inverse.
You define the function K(x) (the blue graph) so that it is the mirror image, in the line y=x (the dotted graph), of f(x) as defined on x<=2 (the red graph). All you have to do is change the place of x and y in y = - 3x + 8 and solve for y to get
\(k(x) =-\frac{1}{3}x+\frac{8}{3}\), x>2.
