To prove that a function is surjective, take an arbitrary element $y\in Y$ and show that there is an element $x\in X$ so that $f (x)=y$. I suggest that you consider the equation $f (x)=y$ with arbitrary …

Nov 12, 2004 · The domain can't be the closed interval, so I don't see how that would help. tan (x) is not defined when x = \pi / 2. Anyways, you know that it is continuous. You know that the limit as x …

To prove a function is bijective, you need to prove that it is injective and also surjective. "Injective" means no two elements in the domain of the function gets mapped to the same image.

Nov 2, 2011 · The discussion centers on proving that if the composition g∘f is surjective, then g must also be surjective. A proposed proof begins by stating that for any z in Z, since g∘f is surjective, there …

May 19, 2021 · In order to prove that a function is surjective you can either prove this directly. Or you can find the inverse function proving that the function is bijective (just like you have done), thus …

Sep 19, 2013 · Homework Statement . Let X, Y be metric spaces and f: X → Y a continuous and surjective function. Prove that if X is separable then Y is separable. The attempt at a solution. I've …

Dec 25, 2006 · how can i prove if f (x)= x^3, where the domain and the codomain are both the set of all integers: Z, is surjective or otherwise...the thing is, when i do the prove it comes out to be surjective …

How to prove that this function is surjective? [duplicate] Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago

Feb 5, 2014 · Prove that a function is surjective bassflow Feb 5, 2014 Function Surjective Feb 5, 2014 #1 bassflow 3 0

Jul 27, 2022 · My thoughts directly went to the inverse function but than I started having doubts because if the domain is bigger than the co-domain the inverse function would have to have more than one …