preimage

1. preimage of a continous function is an interval

To prove: a continuous real-valued function (f) defined on set S has an image (S') that is an interval then S must be an interval. Tools: definition of continuity, definition of a connected set, connected set in R is an interval, If S' is not a singleton; if f(a), f(b) \in S' such that f(a)...
2. image and pre-image of a function/interval

Hi, I'm having a problem with setting the image of a function or interval of a function. I do understand how to calculate the pre-image. Example: f(x) = -x^2 - 3 so to calculate the pre-image of the interval (0,1) I simply calculate 0 = -x^2 - 3 and I get minus square root of 3 and square root...
3. [ URGENT ] anyone can help me solve preimage question ?

Determine the pre-image under f for each of the intervals (i) [-5, -1] (ii) [-5, 0] (iii) [-2, 4] (iv) (5, 10) (v) [11, 17] anyone...
4. Finding the Pre-Image

In f: Z--->N (where N represents natural numbers and Z represents integers. For the function f(x) = 2|x|, find the pre-image of the set {10, 11, 12, ... , 19} Would it be {-9, -8, -7, -6, -5, 5, 6, 7, 8, 9}?
5. Pre-Image / Image proof

I'm new to topology and have a pretty basic proof to perform but haven't had much experience with proofs and could use some help, Question asks, to prove that if f: A -> B and X is a subset of A prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X...
6. Preimages and images

Hi, have a set of questions on preimages and images that I can't do. Here's an example of both: Find the following preimages f−1((−1, 4)) for f : R ! R, f(x) = (x − 1)2. f((1,1)) for f : R : R, f(x) = 1/x
7. Preimage matrix

All I'm wondering is how to write a "preimage" matrix for an object on a coordinate plane. Attached is the question. I can do the rest. :D
8. second preimage resistant

Suppose that f : {0, 1}m Æ {0 1}m is a preimage resistant bijection. Define h : {0, 1}2m Æ {0, 1}m as follows. Given x OE {0, 1}2m, write x = x’ || x’’ where x’, x’’ OE {0, 1}m. Then define † h(x) = f (x'!x''). where is “XOR” operationProve that h is not second preimage resistant. could you...
9. preimage and image stuff

how do you prove the preimage of the image of the domain is equal to the domain and how do you prove the image of the preimage of the codomain is the codomain
10. function with different image, smae preimage

Please give an example of a function f, and two sets U_1,U_2:U_1 \subset U_2, U_1 \neq U_2 but f^{-1} (U_1)=f^{-1}(U_2)? Is there such a function in R^n?
11. Pre-image of an ideal

Essentially, I believe my question boils down to this: does the correspondence theorem at least partially hold for Lie algebras (or, indeed, any algebra)? K, L Lie algebras, K \leq L. Let \phi be some homomorphism of Lie algebras and let K\phi \neq 0 be an ideal of L\phi, K\phi \unlhd L\phi...
12. Onto Proof

Can someone give me some feedback, please? ******** f: Ζ⇒Ζ f(x) = { x/2 if x is even, 0 if x is odd Prove whether f is onto and one-to-one. Here's my proof. ****** Proof. To show that f is onto, let b∈Ζ. Consider the 2 following cases: 1. If b=0, f(x)=0 implies x=z. 2. If b≠0...