Intersecting Bivariate Functions: Is x=a the Only Point of Intersection?

[Saracen Rue]

Will the bivariate function $f(x,a)$ always intersect $f(a,x)$ at the point $x=a$ given that $f$ is a real, defined function? (other points of intersection can exist but are not relevant for this question)

 

[chiro]

Hey Saracen Rue.

If you have an intersection then it means that the two things are equal.

So if you had a bivariate function with points (a,b) and (c,d) then an intersection happens when f(a,b) = f(c,d)

You have specified [if I read correctly] that a=x, b=a', c=a', d=x and a'=x meaning that you have f(x,x) = f(x,x) which is trivial.

Are we missing something here?

 

[mfb]

Didn't we answer that question in your earlier thread already?