Function Transformations  how do I find the invariant points?
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You're looking for points where $f(x)=x$. Phrased differently, you're looking for points where $(x,x)$ lies on your graph. Rephrased once more, you're looking for intersection with the line $y=x$.
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Kat
Updated on January 10, 2020Comments

Kat over 3 years
When they give you a picture of a graph (doesn't matter what kind  linear, parabola, inverse, etc.) how do you find the invariant points?

epimorphic almost 8 yearsPossibly related: Analysis Question? Fixed Point? and Fixed point location for functions

Rock over 5 yearsI believe the question is how to determine invariant points between a function and it's inverse. If you're looking to algebraically find the point, you just make the two functions equal each other, and then solve for x.


Kat almost 8 yearsI get what I am looking for but how do I find it?

Zach Stone almost 8 yearsDraw the line $y=x$, and look for intersection with the given graph.

Kat almost 8 yearsIs there any way to do it algebraically?

Zach Stone almost 8 yearsWait, are you given a picture or equation? If you have the equation, set $f(x)=x$ and try to solve for $x$. I can't be more specific without more details about what $f$ looks like. Sometimes it's possible, sometimes it's not.

Kat almost 8 yearsIt is just a picture of a graph of two porabolas side by side (one is a reflection over the yintercept) that will eventually intersect but do not in the picture.

Zach Stone almost 8 yearsIf you don't have any equations, then you can't do any algebra.