When solving $\arcsin x = \pi \arccos x$ algebraically that gives us solutions that are not true (since the equation has no real solutions. This begs the question: Under what conditions would $f(x)=g(x)$ and $h(f(x))=h(g(x))$ have the same solution sets?
When are $f(x)=g(x)$ and $h(f(x))=h(g(x))$ equivalent?
0
$\begingroup$
functions
trigonometry
elementary-set-theory
-
3When $h$ is injective? – 2017-01-29
1 Answers
0
This holds if and only if $h$ is what's called a "monomorphism", as a category theoretic notion. Now, this is equivalent the category of sets to being injective.