site stats

F x+y f x +f y continuous

WebFeb 21, 2024 · Homework Statement Let f be a continuous function lR (all real numbers) --> lR such that f (x+y) = f (x) + f (y) for x, y in lR. prove that f (n) = n*f (1) for all n in lN (all natural numbers) Homework Equations f is continuous also note and prove that f (0) = 0 The Attempt at a Solution Edit: WebJan 4, 2015 · A function f : X → Y is continuous if, for every x ∈ X and every open set U containing f (x), there exists a neighborhood V of x such that f (V) ⊂ U. Proof: Let C be a closed subset of Y, s.t, C ⊂ Y. Clearly, if C is closed, the set Y-C is open since the compliment of a closed set is an open set (Theorem 6.5).

calculus - Proving that $f(x+y) = f(x) + f(y)$ and $f$ being continuous ...

Web*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers and new subjects. Web2 days ago · Final answer. Transcribed image text: Let the continuous random variables X and 1. At least 5.5 Y be defined by the joint density function f (x,y) = ⎩⎨⎧ 501 0 otherwise for 0 ≤ x,0 ≤ y and x+ y ≤ 10 2. At least 1.5 , but less than 2.5 3. At least 3.5 , but less than 5.5 4. At least 2.5 , but less than 3.5 Determine E[X ∣ Y = 6] 5 ... good morning salutation comma https://fsanhueza.com

metric spaces - Prove that if a function $f: X\to Y$ continuous …

WebMay 23, 2015 · The solution I have is that f is not continuous in . (The solution doesn't say more than that.) However, the result I got is that is continuous in . Here's my approach: Lets transform and into their polar coordinates, so that we can approach from any direction by varying : Then is continuous iff By using the polar coordinates and letting we get: WebSo is continuous. (inverse image of closed is closed). This direction only uses compactness of . For the other direction we only need the Hausdorffness of : The diagonal is closed iff … WebAug 16, 2024 · Also, are we to assume that $f (x)$ is continuous? If not, then I don't believe that $f (xy)=f (x)f (y)\implies f (x)=x^c$. Take, for example, any additive non-linear function, $g (x) $ with $g (x+y)=g (x)+g (y)$. Then $f (x)=e^ {g (\log x)}$ satisfies $f (xy)=f (x)f (y)$. Show 6 more comments You must log in to answer this question. good morning rush

f(x+y) = f(x)f(y) - YouTube

Category:real analysis - prove a function $f(x,y) = \max(x,y)$ is continuous ...

Tags:F x+y f x +f y continuous

F x+y f x +f y continuous

f(xy) = f(x) + f(y), - JSTOR

WebA: given f(x)=x centered at x=4 f(x)=x f(4)=2f'(x)=12x-12… question_answer Q: Find the directional derivatives of the following functions at the specified point for the specified… Webcontinuous then its graph is closed. Ask Question. Asked 9 years, 5 months ago. Modified 7 years, 1 month ago. Viewed 8k times. 12. The graph of f is G ( f) = { ( x, f ( x)): x ∈ X } …

F x+y f x +f y continuous

Did you know?

WebMay 23, 2015 · The solution I have is that f is not continuous in . (The solution doesn't say more than that.) However, the result I got is that is continuous in . Here's my approach: … WebIf we were now to assume that f(x)were continuous, it would follow that f(x)=ekx everywhere, since the closure of Q is R. 4 Measurable functions It turns out to be sufficient to assume that f(x) is measurable or Lebesgue integrable, and not identically zero, in order to obtain exponentials from f(x +y) = f(x)f(y). The proof runs as follows.

WebIt suffices to show that f ′ ( x) = 0 for all x ∈ R. We see that the given condition implies f ( x) − f ( y) x − y ≤ x − y . So in a δ -neighborhood of x, the quotient in definition of the derivative is less than δ. So the limit is 0, and we are done. Share Cite Follow answered Jun 30, 2012 at 5:15 Potato 38.7k 17 126 263 Add a comment WebIf f ( x y) = f ( x) f ( y) then show that f ( x) = x t for some t If f: R → R is such that f ( x + y) = f ( x) f ( y) and continuous at 0, then continuous everywhere continuous functions on …

WebOct 26, 2024 · In this improvised video, I show that if is a function such that f (x+y) = f (x)f (y) and f' (0) exists, then f must either be e^ (cx) or the zero function. It's amazing how we can derive all that ... WebSo now we see that if ( x n, y n) ∈ G ( f), ( x n, y n) → ( x, y), then y n → f ( x n) as defined by G ( f) and x n → x, f ( x n) → y. Since f is assumed to be continuous, f ( x n) → f ( x) so y = f ( x). Therefore ( x, y) ∈ G ( f) and we conclude G ( f) is closed. Share Cite Follow edited Feb 22, 2016 at 22:06 YoTengoUnLCD 13.1k 4 39 99

WebOct 29, 2024 · Question: Let (X, d1) and (Y, d2) be two metric spaces and f, g: X ↦ Y be two continuous functions. Then prove that {x ∈ X: f(x) = g(x)} is closed in X. Approach: We consider the function h: X ↦ R + ∪ {0} defined by h(x) = d2(f(x), g(x)) Lemma 1: h(x) is continuous on X.

WebYou have already shown: if f (x+ f (y))= f (x+ y)+1 and if f is surjective, then f (z) = z + 1 for all z. Now it remains to show that the function given by f (x) = x+1 , is injective and … chess pieces australiaWebf(x + y) = f(x)f(y), f(xy) = f(x) + f(y), f(xy) = f(x)f(y). ... of real-valued continuous functions defined on some topological space. We will also discuss the existence of such functions on A and possible general form of these functions. A dsc-pola, denoted by A, is a real linear associative algebra which satisfies the ... chess pieces boxWebViewed 3k times 2 Consider the function f: R 2 → R given by f ( x, y) = max ( x, y). (That is, f ( x, y) is the larger of x and y, so f ( − 3, 2) = 2, f ( 1, 4) = 4, and f ( − 3, − 2) = − 2 .) … chess pieces bulkgood morning sam good morning ralphWebAug 16, 2024 · So f must be a linear function. The only linear functions Q → Q are of the form f ( x) = a x. For such a function, we must have f ( x + f ( y)) = f ( x) + y; that is, we must have a ( x + a y) = a x + y. So we must have a 2 = 1. So the only functions that could possibly work are f ( x) = x and f ( x) = − x. chess pieces best to worstWebMar 9, 2024 · Let f: R → R be a continuous function such that f ( x + y) = f ( x) f ( y), ∀ x, y ∈ R. Prove: if f ≢ 0, then there exists constant a such that f ( x) = a x. I tried to deduce … good morning sam cartoonWebApr 11, 2011 · The question states: Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a … chess pieces black and white