Intersection of a function and it's inverse

[jasopan]

Hey I was wondering about finding the intersection point of a function and it's inverse.

For non-calculator tests especially, I was given a quadratic and its inverse was a Square-root function.

By equating them, i ended up with a quartic which was way too difficult to solve via hand. In the end I just equated x= <either function>

But what I wanna ask is how do we solve for where the two functions intersection MORE than once?
Because when we assume that they intersect at y=x we are only solving for one solution and I don't know if this applies to all functions.

I remember once where they intersected 3 times and impossible w/o a calculator (for me at least).

Can someone elaborate on this assumption?

[Mao]

Hey I was wondering about finding the intersection point of a function and it's inverse.

For non-calculator tests especially, I was given a quadratic and its inverse was a Square-root function.

By equating them, i ended up with a quartic which was way too difficult to solve via hand. In the end I just equated x= <either function>

But what I wanna ask is how do we solve for where the two functions intersection MORE than once?

Excellent question. Firstly, let me correct you on your wording. By solving for or , you may obtain more than one solutions if the function crosses y=x more than once (e.g. ). You meant why do we only find solutions where they cross y=x?

The answer is there's no good way to check. For the sake of MM, you are pretty safe to bet that they won't give you anything crazy like that, especially not in exam 1. So keep solving and you'll be fine.

But for the sake of interest, graph , its inverse will coincide with itself (thus infinite intersection points). Also try , and , and for

[jasopan]

Yo,
sorry about not being clear, that's what I meant.
That last thing you said looks too complicated for me xD
But thanks for clearing up about how in the MM course we only ever use the intersection of f(x) or f^(-1)(x) with y=x.
Just that in the essentials book there was a crazy question so yeah
-Cheers

[Richiie]

I think you would just let the normal function or inverse function equal to x then solve, because both function intersect each other at the line of y=x.

[the.watchman]

I think you would just let the normal function or inverse function equal to x then solve, because both function intersect each other at the line of y=x.

Not in all cases, some functions intersect with its inverses on the line y=-x as well.
So be careful

[jasopan]

Here's one which intersects once in the line of y=x and twice in some other place



and it's inverse