Function Question

[empty jewel]

I have a question, i’m wondering if you are able to describe the solutions between two functions as the intersection of them, given by,
f(x) ∩ h(x)
where we can just say, f(x) and h(x) are functions that are continuous and differentiable across their entire domain.

Would f(x) ∩ h(x) be the same as f(x) = g(x)?? Would this be mathematically acceptable, regarding finding the solutions of two functions?

Or can you only use intersection for sets, not functions? If so, can you elaborate more on this please.

[quiet bridge]

Technically, functions are sets, so $f(x)\cap h(x)$ is well-defined. However, it would serve almost no purpose in the context you are attempting to use it

[oblique elk]

SWR

[quiet bridge]

hmmm actually

nah you had it right

$f(x)\cap h(x)$ would be the set of all points where $f(x)=h(x)$

[oblique elk]

SWR

[empty jewel]

So, to describe the solutions between two functions, using intersection, would you say

f(x) ∩ h(x) = { (x1, y1), (x2, y2), (…) }

[quiet bridge]

yes

[empty jewel]

Ok thanks

.close