Inverse Definition and 1000 Threads

Homework Statement The function y=x^{2}+4x-6 has two inverses. What are they and which domains lead to these inverses? Homework Equations The Attempt at a Solution y=x^{2}+4x-6 x=y^{2}+4y-6 y(y+4)=x+6 Not really sure where to go from here.

Homework Statement (part of a problem) Find the inverse Fourier of F(w) = (3jw+9)/((jw)^2+6jw+8) where w is the angular frequency, w=2pi * f = 2*pi/T Homework Equations The fourier transfrom and its properties i guess. Also the exponential FT common pair exp(-at)u(t) <-> 1/(jw+a) where...

Homework Statement L^{-1}\{\frac{1}{(s^2+4)^2}\} Homework Equations The Attempt at a Solution I have no idea how to solve this. Any idea to being solving the problem would be appreciated.

Homework Statement My problem is as follows: find the inverse of 3x+1+\sin(x) with the domain [-\frac{\pi}{2},\frac{\pi}{2}] Homework Equations The Attempt at a Solution for this would I just try to solve as normal by setting y=f(x) then using the fact that \arcsin(x) = y or is...

Suppose that a spaceship is fired into orbit from Cae Canerveral. Ten minutes after it leaves Cape, it reaches its farthest distance north of the equator, 4000 kilometers. Half a cycle later it reaches its farthest distance south of the equator (on the other side of the Earth, of course!), also...

Homework Statement Greetings everyone! I am having problems getting started with this question, which asks: Find the inverse of y = \frac{3-4e^x}{6-10e^x} Homework Equations The Attempt at a Solution I'm usually pretty good with these kinds of problems, but for some reason I seem to be...

Homework Statement Inverse Laplacetransform (3s+7)/(s^2+2s-2) Homework Equations (3s+7)/(s^2+2s-2) The Attempt at a Solution Split into 3s/(s^2+2s-2) and 7/(s^2+2s-2). I can't find a fitting transformpair(I use tables/formulas).

The link below shows a circuit and the s-domain equation for I1(s) that I have derived; My question is on the portion of the equation containing the "(s+a)" terms. I am trying to arrive at the time-domain equation for I1(s) but instead of arriving at the Laplace transform pair shown in the...

Hello everyone, I have been using the well-known Cal Tech camera calibration toolbox built by Jean-Yves Bouguet for stereo triangulation. Part of the toolbox's utility is that it's able to give 3D world coordinates from 2D coordinates in stereo image pairs, given a set of camera...

Awhile back A.T. & PeterDonis helped me through several basic confusions on my way to an intuitive understanding of geodesics in curved spacetime. I looked at http://www.relativitet.se/spacetime1.html http://www.adamtoons.de/physics/gravitation.swf...

Homework Statement Compute the inverse Laplace transform of Homework Equations http://img267.imageshack.us/img267/696/66451772.png The Attempt at a Solution I tried using partial fraction but no luck.

I was wondering which are the properties of functions defined in such a way that ∫dx f(y-x) g(x-z) = δ(y-z) where δ is Dirac delta and therefore g is a kind of inverse function of f (I see this integral as the continuous limit of the product of a matrix by its inverse, in which case the...

Hi all, i need help with integration of exponential of inverse tangent, could not find it in table of integrals the whole equation is I=∫A/[w(a+z^2)^1/2]*exp(zb)*exp[(-i*arctan(z/(a)^1/2)] -am trying to integrate by parts but stuck at the arctan part Thank you.

I'm self-studying Calculus and would like to ask some doubts about the following question: Homework Statement If, in t seconds, s is the oriented distance of the particle from the origin and v is the velocity of the particle, then a differential equation for harmonic simple motion is...

f(t)=\int^{c+i\infty}_{c-i\infty}F(s)e^{st}ds Why we suppose that all singularities are left from line Re(s)=c?

Homework Statement Let the DTFT (Discrete time Fourier transform) of a signal beY(f)= {1 0≤lfl< \frac{fs}{8} {0 OtherwiseCalc y(k) Homework Equations y(k)=\frac{1}{f_{s}}\int Y(f) e^{jk2\pi fT}df lkl≥0 The Attempt at a Solution So what I understand from this is that my Y(f) is basically 1...

Homework Statement I'm attempting to find the inverse laplace transform of (5/((2x+3)(4+x^2))) The Attempt at a Solution Here's the solution: http://www.wolframalpha.com/input/?i=inverse+laplace+transform+%285%2F%28%282x%2B3%29%284%2Bx%5E2%29%29%29 There's 3 terms in the solution and 2 are...

Hi, quick question regarding my solution of this Inv. FT: Y(\omega) = \frac{1}{j}[sinc(\frac{2\omega}{\pi} - \frac{1}{2}) - sinc(\frac{2\omega}{\pi} + \frac{1}{2})] Recognizing that that this looks a lot like this property of the FT: x(t)sin(\omega_{0}t) \leftrightarrow \frac{j}{2}[X(\omega +...

Q: Given a fraction A/B when does there exist a finite group G and an automorphism f s.t. exactly A/B elements of G are mapped to their own inverses (f(a) = a-1? If so how can we find the group? Does anything change if we allow infinite groups? I have a friend who was preparing for an intro...

Why is it that the differential cross section for processes like Inverse Muon Decay (IMD) are always given in the CM frame? Every paper I have seen that discusses Inverse Muon Decay gives the differential cross section in CM frame. Is it very hard to calculate the differential cross section in...

Hello, I have been working on this problem for a while now and can't seem to get it into a forum which would isolate x, which would then allow me to sub y and find the inverse. The problem is x^3/x^2+1 Can anyone help me with this? I am utterly stuck I have dealt with a similar...

Homework Statement X(z)=z/(z-.7)^2 Use the residue method to calculate x(k) Hello, I have this exercise that I am trying to complete. I am not really familiar with the residue method and am having a hard time finding a good example on line. The section in my book does not describe it...

Homework Statement If T : V → W is an injective linear transformation, then T^-1: V →W is a linear transformation. The Attempt at a Solution Let w1, w2 in W. If w1=T(v1) and w2=T(v2), v1=/=v2 in V. Thus, T^-1: V →W is a function. Then, v1+v2=T^-1(w1) + T^-1(w2) and for a in F...

Homework Statement Determine if the following function is invertible. If it is, find the inverse function. f (x) = -sin(-x) -∏ < x < ∏ The Attempt at a Solution f(x) = -sin(-x) y = -sin(-x) -(sin y)^-1 = -x (sin y)^-1 = x when x = -∏, y = 0 when x = ∏, y = 0 f^-1(x)...

Homework Statement The Markov matrix A = [.9 .3; .1 .7] has eigenvalues 1 and .6, and the power method uk=Aku0 converges to [.75 .25]T. Find the eigenvectors of A-1. What does the inverse power method u-k=A-1u0 converge to (after you multiply by .6k)? Homework Equations The...

I'm having a little trouble with something so I am wondering, If f is a continuous 1-1 mapping from an open set (a,b) into ℝ then is its inverse function g continuous at all points of the image of f? My argument is that g(y) is in (a,b) for all y in the image of f, and g(y)=x for some x in...

Homework Statement Given the exponential function and its inverse, where a > 0 Exponential Function: f(x)=a^x Inverse function: f^{-1}(x)=log_ax a) For what values of a do the graphs of f(x)=a^x and f^(-1)(x) intersect?The Attempt at a Solution I have no idea how to start this question. Off...

Homework Statement I'm trying to find the inverse function of the following. f(x) = [x^2 - 9]^0.5 x <= -3 The Attempt at a Solution In the book I'm using it gives the inverse function as; y = -(x^2 + 9)^0.5 [0, +∞) Is this correct, as I'm getting an inverse...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Homework Statement Let f : A → B be a function and let Γ ⊂ B × B be an equivalence relation on B. Prove that the set (f × f)^-1 (Γ) ⊂ A × A (this can be described as {(a, a′) ∈ A × A|(f(a), f(a′)) ∈ Γ}) is an equivalence relation on A.Homework Equations The Attempt at a Solution Let...

Homework Statement Find all solutions of inverse sine (-1/2). Angles lie between 0 and 2∏. The attempt at a solution I know it sounds very simple, but i must be having some of the basics wrong, as i can't figure out the second solution. I used the calculator (in radian mode) to find inverse...

Homework Statement F(s) = 3/(s(s^2 +2s + 5)) Homework Equations The Attempt at a Solution I have used partial fraction using coefficients. F(s) = (3/5)s - (3/5) ((s+2)/(s^2 +2s + 5)) and reduce s^2 +2s +5 by completing the square F(s) = (3/5)s - (3/5) ((s+2)/((s+1)^2 + 4))...

the definition of a green's function is: LG(x,s)=δ(x-s) the definition of a right inverse of a function f is: h(y)=x,f(x)=y→f°h=y how does it add up?

I am self-studying Calculus and tried to solve the following question: Homework Statement Suppose that the function f is continuous and increasing in the closed interval [a, b]. Then (i) f has an inverse f-1, which is defined in [f(a), f(b)]; (ii) f-1 is increasing in [f(a), f(b)]; (iii) f-1...

How do find the inverse Fourier Transform for the following using the transform pairs and properties? X(jw) = 1 / (2 - w^2 + j3w) Thanks!

Homework Statement Find the inverse of this function f(x) = x^3+2x-1 Homework Equations The Attempt at a Solution I'm not able to state the function explicitly. f(x)=x^3+2x-1 y=x^3+2x-1 (switch all x's and y's to find inverse) x=y^3+2y-1 y^3+2y=x-1 y(y^2+1)=x-1...

Hi everyone, I am stuck with this problem. I am looking for E(1/(1 + e^Z)) where Z is a normally distributed random variable. I know that E(e^Z) and E(1/e^Z) follow lognormal and inverse lognormal distibution and the means of these distributions are standard results. Of course, is also...

Homework Statement the questions asks to determine inverse laplace transform of s/(s+4)^4 Homework Equations The Attempt at a Solution this can supposedly be done just using laplace transform tables so I am guessing i need to simplify that to something that's workable but i...

Homework Statement ∫5/(4x√(9-16x2)dx Homework Equations I am pretty sure this is in the form of ∫du/(u√(a2-u2) The Attempt at a Solution setting u=4x a=3 and du=4dx so 1/4du=dx I get: -5/12 sech-1(4x/3) + C Is this right or am I using the wrong definition? Just trying to...

I have a basic question about the spin hall effect and the inverse spin hall effect (SHE): Let's take a material like Pt, which has a high SHE. Typically the spin hall conductivity (spin current over electric field) = 300 ohm^-1 cm^-1. However, it is also used for measurements using the...

Hello, how to find matrix 4x4 which only contains whole numbers and has inverse matrix with whole numbers only aswell? Is there algorithm to find such matrix of n*n? Thanks.

My contention is that you cannot apply the Inverse Function Theorem to this problem because there is a point in the interval at which the derivative is zero. At x = pi/2, f ' = 0. http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled.png

Homework Statement Let f:A->B and g:B->C be invertible mappings. Show (g o f)^-1 = f^-1 o g^-1. Homework Equations A mapping is invertible iff it is bijective The Attempt at a Solution I understand why these are equivalent statements; however, I can't figure out the wording of the...

Homework Statement For exercises 49 and 50 let f(x) = (ax + b)/(cx + d) 50. Determine the constants a, b, c, d for which f = f-1 Homework Equations I found in question 49 when they asked to find f-1 that: f-1 = (dx - b)/(a - cx) This was also the answer at the back of the book but...

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Homework Statement Derive an equation to represent the current flowing in an RLC circuit where R=12 L=1.2 C=30microfrards with an impulse voltage input. Assume zero conditions when the switch is closed. Homework Equations The Attempt at a Solution I have used the voltage to equal...

Homework Statement Using Octave or Matlab solve random binary matrices(with 1s and 0s) of size N and plot them together. Draw a conclusion. The Attempt at a Solution http://img703.imageshack.us/img703/7803/plotm.png I was just wondering if this looks correct to you. I previously had...

Homework Statement http://img847.imageshack.us/img847/2783/77597781.jpg Homework Equations See below. The Attempt at a SolutionI get all the way to the last step, but I'm not sure how to perform it.I get to the point where I have: [(T^-1)(ax^2+bx+c)]\alpha= [T^-1]\alpha\beta*[v]\beta= [ a/4...

Given the following cross product equation: \vec{A}\times\vec{B}=\vec{C} How to express \vec{A} in term of \vec{B} and \vec{C} (or \vec{B} in term of \vec{A} and \vec{C} ). I think the question I want to ask can also be rephrased as if one was told that a known vector when cross product with...