Inverse Definition and 1000 Threads

Homework Statement Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4). Homework Equations I don't want to find the answer by looking at the Table. F(s)=2s/(s^2-4)-3/(s^2-4) The Attempt at a Solution The answer is f(t)=2 cosh 2t - (3/2) sinh 2t.

Hi I have a question regarding differentiation of inverse functions that I am not capable of solving. I want to prove that \frac{\partial}{\partial y} h_y(h^{-1}_{y_0}(z_0))\bigg|_{y=y_0} = - \frac{\partial}{\partial y} h_{y_0}(h^{-1}_{y}(z_0))\bigg|_{y=y_0}, where h_y(x) is...

Hello, I have the following matrix of matrices \mathbf{H}=\begin{array}{cc}\mathbf{A}&\mathbf{B}\\\mathbf{B}^H&\mathbf{A}\end{array} where each element is a square matrix, A is a diagonal matrix of real numbers, whereas B is not (necessarily), and the superscript H means conjugate transpose...

Write the inverse, converse, and contrapositive of the following statement: upside down A x E R, if (x + 2) (x - 3) > 0, then x < -2 or x > 3 Indicate which among the statement, its converse, its inverse, and its contrapositive are true and which are false. Give a conterexample for each that...

Let f(x) = k\ log_2 x (a) Given that f^{-1}(1)=8, find the value of k to get f^{-1}(x) exchange x and y x=log_2 y^k then convert to exponential form 2^x=y^k then 2^{\frac{x}{k}} = y so for f^{-1}(1) = 2^{\frac{1}{k}}= 8=2^3 then \frac{1}{k}=3 so k=\frac{1}{3} (b) find...

Do we have identities for the following \arctan(x+y) = \arctan(x)-\arctan(y) =

Let's say we have a one dimensional single particle system that is described by a SE -\frac{\hbar^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi(x)+V(x)\psi(x)=E\psi(x) We do not know what the potential energy function V(x) is, but we know that the eigenvalues spectrum is E_{n}=kn^{\frac{3}{2}}...

"All engineers have practical skills or are good at mathematics" to write down the converse, inverse and contrapositive for the above statement, I have to find the hypothesis and the conclusion of the statement. but how? is there any other way to write converse, inverse and contrapositive...

Checked around a buch and could not find any help. But I needed help with: Understanding that if I get the Inverse FT of K-space data, what is the scaling on the X-space (object space) resultant image/data i.e. for every tick on the axis, how do I know the spatial length? More detailed...

Having difficulty with L-1 {1/(s^2+s-20)}: Should I make it L-1 {1/(s+5)(s-4)}? I'm stuck.

Homework Statement Let L: V →V be a linear mapping such that L^2+2L+I=0, show that L is invertible (I is the identity mapping) I have no idea how to solve this problem or how to start,I mean this problem is different from the ones I solved before, the answer is "The inverse of L is -L-2 "...

what is the inverse laplace transform of (2s)(1/(s-2))? could i use the identity ∫f(T)g(t-T)dT=F(s)G(s)? i was hesitant so i figured i'd just ask before i continue..

I just came across Seebeck effect and Inverse Seebeck effect. It says that when electric current is passed through or if electric voltage is applied between a Seebeck couple heat is dissipated at one end and absorbed at the other. By assuming that heat dissipation refers to heating and heat...

OK, this is one where I am having trouble starting because I am not sure I am reading the question correctly to begin with. So start with: M_{m×n}(K) denotes the set of all matrices with m rows and n columns with entries in the field K. Let β⊂V and β′⊂W be bases of vector spaces V and W...

Hi there, I'm learning about solitons and chanced upon this pdf talking about the inverse scattering method. However, I'm stuck trying to derive the coefficients using the LAX method (pg 5 of the attached pdf or from http://arxiv.org/pdf/0905.4746.pdf). Hope that someone can help shed some light...

If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)? Thank you!

I can find inverses using an adjust for a 3X3 matrix. But My homework book asks us to find the inverse using an adj(A) for a 4x4 matrix. 1 3 1 1 2 5 2 2 1 3 8 9 1 3 2 2 it seems less time efficient to find the inverse using this method. Is it possible to reduce the matrix to a a simpler yet...

I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are I_3 \pm dI_3 The problem is that i'd lke...

Is there a way without using the algorithm to find A-1 of a square matrix greater than 2x2? The question we are given in the books is: [-25 -9 -27] [536 185 537] [154 52 143] We are asked to find A-1 of the second and third column without computing the first column. (Sorry...

Homework Statement Find inverse of each. 1. y<x+1 2. y=2x/(x-2) Homework Equations Switch y and x? The Attempt at a Solution For 1. I switched y and x, so x<y+1. Do I have to switch the sign also? For 2. I switched y and x, so x=2y/(y-2). But I have to express the inverse...

Homework Statement Find the inverse Fourier transform of F(jω) = cos(4ω + pi/3)Homework Equations δ(t) <--> 1 δ(t - to) <--> exp(-j*ωo*t) cos(x) = 1/2 (exp(jx) + exp(-jx))The Attempt at a Solution So first I turned the given equation into its complex form using Euler's Formula. F(jω) = 1/2...

In www.mathhelpforum.com and interesting question has been proposed by the user misiazeska the 05 20 2013...How to find the inverse of this function?...$$y= 5\ x^{3} - x^{5}$$ ... and the unanimous answer has been '... it doesn't exist any closed formula to find x as function of y...'. In my...

Homework Statement Let f be a real valued differentiable function defined in (-1,1). If f(0)=2 and f'(x)=f(x)+e^x(\sqrt{x^4+1}) , then find \frac{df^{-1}(x)}{dx} at x=2. Homework Equations The Attempt at a Solution \frac{dy}{dx}=y+e^x \sqrt{x^4+1} \\ dy=(y+e^x \sqrt{x^4+1})dx...

I was just wondering if inverse functions only apply to one-to-one functions?(Or a function who's domain has been restricted to act as a one-to-one function). Thanks.

I posted it in math, But I think maybe it is more physics then math... Hello, I'm trying to understand the algorithm(‘‘juggling search’’) used in the following article : http://www.cns.atr.jp/~kawato/Ppdf/1...00105-main.pdf In short they have a model of IO cells that are connected...

I am trying to simulate and animate inverse dynamics. So I need to calculate torques. I started out by just taking a rod which rotates about its COM, applied a torque and then just used \tau=I\alpha to make sure I get back the same torque I applied. Next, I attached the rod to the ground with...

Hello MHB, I got one question, I am currently working with an old exam and I am suposed to draw it with vertican/horizontal lines (and those that are oblique). f(x)=\frac{x}{2}+\tan^{-1}(\frac{1}{x}) for the horizontel line \lim_{x->\infty^{\pm}}\frac{x}{2}+\tan^{-1}(\frac{x}{2}) Is it enough...

Inverse curves related to JFET characteristics, help! Hi, This is an example given in a lesson which is closely related to a coursework question I'm trying to complete, the problem is I can't understand how they have got the results they have. Here is the statement giving the relationship...

Homework Statement Find the solution of the givien initial value problem and draw its graph y''+2y'+2y = δ(t-π) y(0) = 1, y'(0) = 0 Homework Equations A Laplace transform chart would be very useful The Attempt at a Solution I chose to solve the equation with Laplace...

Derivatives of inverse functions--how two formulas relate? Homework Statement I know two formulas for calculating the derivative of an inverse function, both of which I know how to derive, but I don't know how to relate them to one another. Homework Equations...

f(x)=a+4/(x-a) f-1(x)=(a^2-ax-4)/(a-x) Which of the following is true? The function is the opposite of its own inverse for any value of a. The function is its own inverse for positive values of a only. The function is the reciprocal of its own inverse for positive values of a only. The...

I'm working on an inverse kinematics problem (I make video games), and I'm reaching a bit beyond my education. Right now, I've got an algorithm that solves the basic IK equation for a chain of rigid bodies connected by joints by approximately inverting ##J\Delta\theta = e##. Where ##\theta##...

Here is the question: Here is a link to the question: Prove the identity, pre calc!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement 5. (a) The functions f and g are defined by f : x|→ 2x + ln3 (x is a real number) g : x|→ e^3x (x is a real number) i) Find f^-1(x) and g^-1(x) and state their domain of definition ii) Show that f^-1 f = f f^-1 = x (x is a real number) iii) Find the composite function...

is this true? (1/ηαβ∂α∂β)= ηαβ∂α∂β any help,pls!

Hi Guys, I am doing a bit of work with dynamic light scattering (DLS) data. It is one of the many areas of science where we encounter an inverse problem. The forward problem is: For a known sized particle, calculate its scattered spectrum (that is easy). The inverse problem is: from the...

For some polynomial functions it is useful to logarithmize both sides of the eq. First. How can this be applied for inverse trig functions? Is it even possible?

I've been wondering whether the Laplace transform is injective. Suppose I have that \int^{∞}_{0}e^{-st}f(t)dt = \int^{∞}_{0}e^{-st}g(t)dt for all s for which both integrals converge. Then is it true that f(t) = g(t) ? If so, any hints on how I might prove it? Thanks! BiP

Find the derivative of y = arctan(x^(1/2)). Using the fact that the derivative of arctanx = 1/(1+x^2) I got: dy/dx = 1/(1+abs(x)) * (1/2)x^(-1/2) But my textbook gives it without the absolute value sign. I don't understand why because surely x^(1/2) squared is the absolute value of x...

Homework Statement Suppose f is a function defined on a set ##S## in ##ℝ^n## and suppose ##Q## is a limit point of ##S##. If ##f(P) → 3## as ##P → Q## prove from first principles that ##\frac{1}{f(P)} → \frac{1}{3}## as ##P → Q##. Homework Equations The Attempt at a Solution...

Homework Statement I am trying to work out the inverse Laplace transform of t^2*u(t-a). Homework Equations The Attempt at a Solution I have been old that it starts (t-a)^2*u(t-a)... which I understand is substituting for (t-a). But I cannot seem to work out the rest can...

Homework Statement L-1{\frac{s}{s^2+4s+5}} Homework Equations \frac{s-a}{(s-a)^2+k^2} \frac{k}{(s-a)^2+k^2} The Attempt at a Solution I completed the square for the denominator and got: L-1{\frac{s}{(s+2)^2+1}} (a= -2, k=1) But how do I get rid of the s in the numerator? Or do I have...

I'm working on showing that Z3 is a ring. The one portion I'd like to confirm is the additive inverse part. So here's what I'm thinking as my proof: Given [x]3 , suppose [3-x]3 is the additive inverse in the set Z3 . Thus: [3-x]3 = [3]3 + [-x]3 = [0]3 + [-x]3 = [0-x]3 = [-x]3 Then, it...

I have been given a question by my tutor to try out for our next class Using the axioms for addition of numbers give a natural language proof that the additive inverse of a number is unique, that is prove: ∀x∀y∀z (x + y = 0) ^ (x + z = 0) → (y = z) I am new at writing proofs! My...

Homework Statement 1. Show that the function f(x) = x5 -x3 +2x is invertible. Compute the derivative of f-1 at 2. The Attempt at a Solution To find f-1 I switched x and y which gave me x = y5 - y3 + 2y this is where i got stuck because I am not sure how to solve for y after that...

Hi Everyone, For an individual inquiry and formal lab report task at school I have chosen to conduct an experiment to find out whether hot shoe mounted flash units follow the inverse square law and how the flash zoom is affected by the inverse square law. My first question is that In order...

I need to prove sin^{-1}(ix)=2n\pi\pm i log (\sqrt{1+x^2}+x) I can prove sin^{-1}(ix)=2n\pi+ i log (\sqrt{1+x^2}+x) How to prove the other part. Please help

Hello, I would like to learn how to calculate and simulate in Matlab inverse kinematics of manipulators.Can you please advise me some good websites or books. I am a beginner. Thanks for any advice.

Homework Statement Let p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3) be a cubic polynomial in 1 variable \lambda. Use the inverse function theorem to estimate the change in the roots 0<x_1<x_2<x_3 if a=(a_2,a_1,a_0)=(-6,11,-6) and a changes by \Delta...

\nabla \cdot \frac{\mathbf{r}}{|r|^3}=4 \pi \delta ^3(\mathbf{r}) What's the proof for this, and what's wrong with the following analysis? The vector field \frac{\mathbf{r}}{|r|^3}=\frac{1}{r^2}\hat{r} can also be written \mathbf{F}=\frac{x}{\sqrt{x^2+y^2+z^2}^3}\hat{x}+...