Function intersection

[Jan 11]

I checked on several functions that the HP Prime finds places where two different functions f (x) meet. If we have two functions: f (x) and g (x) and we create one function from them: f (x) - g (x) = 0 or g (x) - f (x) = 0, then it also finds the zeros of such functions. In the case of the analyzed functions, y = LN (x ^ 2-1) and y = x ^ 2-2, unfortunately, it does not define the contact points of both functions. This is an exceptional case. But when we create a function, e.g. y = x ^ 2-2-LN (x ^ 2-1) or y = LN (x ^ 2-1) -x ^ 2 + 2, then the calculator will find the zeros or extremum (because in in such cases, the null sites are also the extreme sites of function). See the screenshots.