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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.

Jun 13, 2021

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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.

Jun 15, 2021