# Tagged Questions

Sasy $f:\mathbb R\to\mathbb R$ define by $f(x)=x^5$ This is definitely injective as $x_1^5=x_2^5 \implies x_1=x_2$ I say it is surjective because for all really $x$ there is all real $y$, $x \in ... 4answers 43 views ### Set of all matrices with determinant 0, non-zero I was assigned this problem in class: Let$f: M(n, \mathbb R) \rightarrow \mathbb R $be given by$f(X) = det(X)$. Identify the sets$f^{-1}(0)$and$f^{-1}(\mathbb R^*)$, where$\mathbb R^*$denotes ... 2answers 200 views ### Can someone please help with my inverse function and sets discrete math problem? To save me some time writing everything out in latex, I'm adding a picture of the question and Ill try to explain what I understand for the problem. Just a heads up, I'm really not sure how to do this ... 0answers 414 views ### Left inverse iff injective; right inverse iff surjective For a function$f:A\to B$, the function$g:B\to A$is called: a left inverse for$f$if$g\circ f$is the identity on$A$(i.e.,$g\circ f = {\rm id}_A$); and a right inverse for$f$if ... 1answer 57 views ### Composition of function with it's inverse on subdomains I have a short question. We have to check the following statements and tell for which one the equal sign holds. Let$M \subset \mbox{domain } f$and$N \subset \mbox{Im } f$. ... 2answers 56 views ### One-to-one functions between vectors of integers and integers, with easily computable inverses I'm trying to find functions that fit certain criteria. I'm not sure if such functions even exist. The function I'm trying to find would take vectors of arbitrary integers for the input and would ... 7answers 140 views ### How should I understand$f^{-1}(E):=\{x\in A:f(x)\in E\}$? I understand the concept, but I still can't figure out how to read the notation: $$f^{-1}(E):=\{x\in A:f(x)\in E\}$$ I understood the concept due to the examples, not with the notation. Can someone ... 1answer 138 views ### Left inverse of a function Let$f$be the function$f\colon \mathbb{N}\rightarrow\mathbb{N}$, defined by rule$f(n)=n^2$. Needed to find two left inverse functions for$f$. I know only one: it's$g(n)=\sqrt{n}$. Does anyone ... 1answer 179 views ### Inverse image of disjoint is disjoint? If I have two sets that are disjoint i.e.$A\cap B=\emptyset$, and$\varphi \in C^1(U,\mathbb{R}^N)$, then are the inverse images (i.e.$\varphi^{-1}(A), \varphi^{-1}(B)$) also disjoint? My logic ... 3answers 319 views ### Inverse function requirements Let f be an injective function, that is:$f : X \rightarrow Yf(a) = f(b) \implies a = b$Now, my question is, does the following need to hold in order for function to be injective:$(\forall x ...
If I have $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f$ is onto and $f\circ f\circ f = f$, how can I prove that $f$ is bijective? I know that I only have to prove that it is 1-to-1 because I'm ...