How do I find inverse of own piecewise function?

[HighSchoolDx]

So, I have a piecewise function.

f(x) = x^2 - 6x + 12 IF x <= 3.
f(x) = k(x) IF x > 3

I have to find k(x), so that. f will be its own inverse.

How do I do this? I found the inverse of x^2 - 6x + 12 as y = 3 +- sqrt(x - 3). Will that help me here? Help is appreciated!

 

[Dr.Peterson]

So, I have a piecewise function.

f(x) = x^2 - 6x + 12 IF x <= 3.
f(x) = k(x) IF x > 3

I have to find k(x), so that. f will be its own inverse.

How do I do this? I found the inverse of x^2 - 6x + 12 as y = 3 +- sqrt(x - 3). Will that help me here? Help is appreciated!

Yes, you're doing well so far.

Sketch the graphs of [MATH]y = x^2 - 6x + 12[/MATH] and [MATH]y = 3 \pm \sqrt{x - 3}[/MATH]. Then highlight the relevant part of the former, and see how you can use the latter to accomplish the task. (I'm assuming you know what a self-inverse function looks like.)

Show us your graph.

 

[HighSchoolDx]

Sir Peterson,

Thank you for your response!!! I figured out the answer from it. )
I do not have an easy way to take a picture of my papers. (I am on a PC (
So I knew that the inverse will be reflected of x^2 - 6x + 12 will be reflected over y = x. i sketched the 3+- sqrt(x - 3) using the + and - functions. I found that the - version is basically the reflection over it!!! Thus k(x) = 3 - sqrt(x -3)

Thank you so much again!!!

 

[Dr.Peterson]

Sir Peterson,

Thank you for your response!!! I figured out the answer from it. )
I do not have an easy way to take a picture of my papers. (I am on a PC (
So I knew that the inverse will be reflected of x^2 - 6x + 12 will be reflected over y = x. i sketched the 3+- sqrt(x - 3) using the + and - functions. I found that the - version is basically the reflection over it!!! Thus k(x) = 3 - sqrt(x -3)

Thank you so much again!!!

That's right. Here's my graph showing the given function in red (with the excluded half broken), and your function k in green (with the rejected upper half broken):



The solid green is the inverse of the solid red, and it happens that the broken red is the inverse of the broken green, neither of which is part of the problem. The self-inverse piecewise function is the union of the solid parts.