Inverse Definition and 1000 Threads

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...

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...

Does anyone know of a good resource for these types of problems? I took an Intro to Real Analysis class as an undergrad and didn't do so well in it, but now I am working back through the book, and it is making A LOT more sense than it did back then. However, I was looking for some worked...

Homework Statement Let, f(x) = x^3 - 3x^2 - 1 , x => 2 . Find the value of df^-1/dx at the point x=-1=f(3)Homework Equations The definition states; "If f has an interval I as domain and f'(x) exists and is never zero on I, then f'(c) is diff at every point in its domain. The value of (f^-1)' at...

How does one edit the input sequence and the results so as to be able to calculate the inverse dft with the dft algorthm?

According to the Wikipedia page, the inverse Laplace transform is f(x) = \frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} F(s')e^{s'x}ds' Something seems wrong though. If I were to take the Laplace transform this equation, I should get F(s) coming out of the right hand side...

Homework Statement 2 problems, i solved both of them but I am not 100 % I am right Find all points on the curve y=x-2cosx where the tangent line to the curve is parallel to the line y=x and write an equation of the tangent line at such point Let f^-1 be the inverse of the one -to- one...

Diagonalizing an N × N matrix H involves writing it as H = UDU† where D is a diagonal matrix, with diagonal elements equal to the eigenvalues of the matrix H, and U is a unitary matrix. We may write: D= (λ1 0 0 ... 0) (0 λ2 0 ... 0) (0 0 λ3... 0) (... ... ... ... λn)...

Homework Statement Hi! I tried to get the inverse Fourier transform of the function: X(j\omega)=1/(jw+a) for a>0, using the integral: x(t)=(1/2\pi)\int_{-\infty}^{+\infty} X(j\omega)e^{j\omega t}d\omega I know that the inverse Fourier transform of X(j\omega) is...

Homework Statement Find f^{-1}(x) if f(x)=x^{2}-8x+8 and x\leq4 The Attempt at a Solution I set y=x^{2}-8x+8, and then switch y and x to get x=y^{2}-8y+8. I then try solving for y, but I end up with y's on both sides of the equation: x=y^{2}-8y+8 x-8=y^{2}-8y x-8=y(y-8)...

Homework Statement find a formula for f-1 when f is defined by f(x) = 3x+5/x-4 Homework Equations The Attempt at a Solution Here is what I've done so far: First I switch the x and the y so I get x=3y+5/y-4 x(y-4)=3y+5 xy-4x=3y+5 xy=3y+4x+5 xy-3y=4x+5 y-3y=4x+5/x -2y=4+5...

Homework Statement Find the derivative: y=sec-1(1/2t3) Homework Equations \frac{\frac{du}{dx}}{|u|\sqrt{u^2-1}} The Attempt at a Solution I have an example to follow, but I don't know how step 1. became step 2.?...or more exactly the last part under the radical? (1-4t^6) instead...

Homework Statement If y=(1,0,0,0) and F4*c=y, find c. Homework Equations c=F4-1*y The Attempt at a Solution I'm stuck. I don't know how to get F4-1. F4-1 = (1/N) * [1, 1, 1, 1; 1 -i (-i)^2 (-i)^3; 1 (-i)^2 (-i)^4 (-i)^6; 1 (-i)^3 (-i)^6 (-i)^9] (this...

Homework Statement Find the Inverse Laplace Transform of \frac{1}{s}*\frac{\sqrt{s}-1}{\sqrt{s}+1} The Attempt at a Solution for this question i found the singularities to be at 0 and when s = 1. (as the sqrt of 1 is ± 1) there is also a branch point that runs from 0→-∞. so if you...

I have a tricky integral of the form ∫∫[(L^4)((k_z)^2 + (k_p)^2)^2]/[(L^4)((k_z)^2 + (k_p)^2))^4 + (k_p)^2] * e^(i*k_z*z)*e^(i*k_p*cos(θ-θ_k))*dk_z*dk_p which is arising in an inverse Fourier transform. I know that integrals somewhat like this appear in smectic liquid crystals but I can't...

Homework Statement Find the inverse Laplace Transform of \frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1} Homework Equations The complex inversion formula (well known) The Attempt at a Solution The first thing is finding singularities and branch points and so on. From the \frac{1}{s}...

Homework Statement Find all r so that the matrix \begin{bmatrix} 2 & 4 & 2 \\ 1 & r & 3 \\ 1 & 2 & 1\end{bmatrix} is inversable.Homework Equations Gauss-Jordan elimination on a matrix augmented with an identity matrix.The Attempt at a Solution \begin{bmatrix} 2 & 4 & 2 & | & 1 & 0 & 0 \\ 1 & r...

I'm doing an experiment today in class and I just wanted to know what's the inverse of conductance (expressed in S) and its units in the SI system. Thanks for viewing!

Homework Statement Find a section of the graph that is one-to-one and find the inverse of the graph for that domain. The Attempt at a Solution Well I've set the domain to all real numbers greater than 0. This makes the function one to one right? Now how do you find the inverse of the...

Homework Statement For the functions: x = r*cos(θ) y = r*sin(θ) Calculate dθ/dX * dX/dθ (considering θ as a function of x, y) and simplify. The Attempt at a Solution I believe this should always be 1, by definition (as the product of a derivative and its inverse). However, I...

well, i have to prove that the inv. Fourier transform of a gaussian (e^(-(k^2/2)) is a gaussian, i know some elementary complex analysis(never actually taken a class in it), not well enough, it seems, to find the solution to this. I tried to integrate over a circular contour, and let the radius...

Homework Statement Find the inverse laplace transform of the equation listed: (\frac{1-e^{-sa}}{a})*(\frac{1}{s^2}-\frac{RC}{s}+\frac{sRC+R^2\frac{C}{L}-1}{s^2+s\frac{R}{L}+\frac{1}{LC}}) Homework Equations a, R, C, and L are constants. The Attempt at a Solution Completely...

Homework Statement Any way to reduce this function for simplification? (Trying to find the reverse Laplace function) I found this function after doing a circuit analysis on a transmission line. \frac{s^2RC+sL}{s^2RC+sL+R} Homework Equations noneThe Attempt at a Solution I couldn't...

What's the point of logarithms when trying to sketch functions? Isn't y=3^x the same as x=3^y? I think it should be the same, but I get different results for each method. If it is the same, what's the point of y=log3x? It's confusing and I don't get the same results when trying to find the...

To determine if a matrix is invertible or not, can we determine this by seeing if the determinant of the matrix is zero or non-zero ? If it's zero, then the matrix doesn't exist because the inverse of the determinant would be an infinite number ?

Homework Statement PLEASE HELP. HOMEWORK DUE TOMORROW. Let N denote the set {1, 2, 3, ...} of natural numbers, and let S:N-->N be the shift map, defined by S(n) = n + 1. Prove that S be no right inverse, but it has infinitely many left inverses. Homework Equations Some definitions. If an...

I'm doing some really basic cycle homework, and in doing an exercise, I noticed something which is what i was probably supposed to notice but I want to know if my conclusion is correct. "all mappings from N to N (N=finite subset of naturals) that can be written with exclusively 1 or 2...

(Matlab) How to find inverse using "eig" I'm doing a project for Numerical Methods and one of the questions is how to find an inverse of a (random) matrix using Matlab function 'eig'. I know the solution is probably simple, but I almost never used Matlab before, besides, lectures were horrible...

I am studying the very first chapter of analysis, but can't quite get through this problem: Prove f −1(f(A)) ⊇ A Prove f(f −1(B)) ⊆ B

Homework Statement Give the inverse of this function N=f(L)=1816-8L The answer has to be filled in in Maple Homework Equations The Attempt at a Solution N=1816-8L 16-8L=ln(N)/ln(18) -8L=(ln(N)/ln(18))-16 L=-ln(N)/(8*ln(18))+2 Is this correct? When i fill...

Homework Statement Find x as a function of y, if y = (2x^2+x+1)/(2x^2+x-1) Homework Equations (1/8 (-4 i x+sqrt(7)-i) (4 i x+sqrt(7)+i) ) / (x+1) (2 x-1) for 2x^2+x+1, how do I factor that out to get 1/8 (-4 i x+sqrt(7)-i) (4 i x+sqrt(7)+i)? quad. formula? The Attempt at a...

Homework Statement Find the inverse Laplace transform of \frac{2s+1}{s^2-2s+2}Homework Equations The Attempt at a Solution \begin{align*} L^{-1}\{ \frac{2s+1}{s^2-2s+2} \} &= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + L^{-1}\{ \frac{1}{(s-1)^2+1} \} \\ &= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + e^t...

1. a) Prove the following holds for A A is a matrix [a b, c d] I is identity matrix. A^2 = (a+d)A-(ad-bc)I. b) Assuming ad-bc not equal to 0, use a) to obtain an expression for A^-1. The Attempt at a Solution I proved the first equation, but I'm not seeing where it relates to...

Homework Statement derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x Homework Equations sinhx=(e^x-e^-x)/2 ? The Attempt at a Solution i have been staring at this for awhile and i don't know how to start what should be the first step towards deriving that...

so for a mapping f:X->Y where X,Y are Normed Vector Spaces if I have a function f(x) = y such that x in X and y in Y, how do I explicitly find f inverse? I sat down to do this and realize I've only been trained in the Reals where you switch the x,y and then solve for y. But this won't...

Homework Statement Let f(x) = 2x^3 + 5x + 3 Find the inverse at f^-1(x) = 1 Homework Equations N/AThe Attempt at a Solution The only way that I know how to solve inverses is by solving for X, then replacing it by Y. Then I supposed I would sub 1 into the inverted polynomial. However I'm...

Homework Statement f(x)= x+cosx find the inverse, f^-1(x) The Attempt at a Solution To start, I tried to solve the original equation for x. But this is where I am having trouble. How do you get x by itself when it is trapped within the cos function? I used to know how to do...

Good day to all, I encounter this expression in analyzing my equation after transform it using Laplace Transform, to get the answer I have to invert it back, I have no idea on how to find its inversion. [text]-\text{Cosh}\left[\sqrt{2 s+s^2} x_0\right]+\text{Cosh}\left[s h_0+\sqrt{2 s+s^2}...