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## Main Question or Discussion Point

ummm, silly question I suppose(and one with likely no answer), and I don't know which Maths subforum to put it in. It's not a pressing thing, just a curiosity.

How do I find the equation of a section that is the overlap of two functions? Not the area of such a section(which would be using Integral), but the equation for it.

e.g I have two functions

y=x^2-4x+5

y=-x^2+6x-4

Now I can tell a program to draw this overlap using

y=[x^2-4x+5,-x^2+6x-4]{(5-sqrt(7))/2<x<(5+sqrt(7))/2}

But I would much rather have an equation proper.

Is this at all possible?

How do I find the equation of a section that is the overlap of two functions? Not the area of such a section(which would be using Integral), but the equation for it.

e.g I have two functions

y=x^2-4x+5

y=-x^2+6x-4

Now I can tell a program to draw this overlap using

y=[x^2-4x+5,-x^2+6x-4]{(5-sqrt(7))/2<x<(5+sqrt(7))/2}

But I would much rather have an equation proper.

Is this at all possible?