Inverse Definition and 1000 Threads

Hi, I'm specifically trying to compute (VΔYT)-1, where V is nxn and orthogonal, Δ is diagonal, and Y is nonsingular. In general we have (AB)-1 = B-1A-1 But how do we do this in general for many matrices? Is there a method, and as long as the matrix dimensions agreed, does the...

f is a one to one function with inverse f^-1, and we are asked to find the inverse of s(x)=[1+f(x)]/[1-f(x)] My attempts leave me with s^-1(x)= [f^-1(1-x)]/[f^-1(-x-1)] and I don't think this is correct. I can't find any examples of problems like this online.

Why is Baye's theorem called "inverse prob"? What is the reason for calling Baye's theorem as "inverse probability"? Any valid reason? Thanks a lot

I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem: Question: Given the Fourier transform of an aperiodic signal X(ω) = 2*sin(3(ω-2π))/ω-2π (a)find its inverse Fourier transform x(t) using...

so here's the question: if you have some equation relating a function, f(x), and its inverse, f-1(x), can you solve for the function? for example, solve for f(x): f(x)+f-1(x)=x^2 how about: f(x)+f-1(x)=g(x) my math teacher (AP calc) was stumped on this one... any thoughts?

I have to take the inverse laplace transform of the above function. Now, I know that I can factor (s^2+5s+6) as (s+3)(s+2) and take the easy way out. However, I did it as above on a test, getting A = -1, B = -1, and C = 1. I then took the inverse laplace transform and got something involving...

hi there I'd like to show that the sphere \mathbb{S}^n := \{ x \in \mathbb{R}^{n+1} : |x|=1 \} is the one-point-compactification of \mathbb{R}^n (*) After a lot of trying I got this function: f: \mathbb{S}^n \setminus \{(0,...,0,1)\} \rightarrow \mathbb{R}^n (x_1,...,x_{n+1})...

Homework Statement Prove in general that if m does not equal n, then AB and BA cannot both be identity matrices, where A is mxn and B is nxm. Homework Equations None (that I know of at least). The Attempt at a Solution At first I thought it would be a good idea to define each...

Homework Statement Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. Homework Equations The Attempt at a Solution I really don't know how to do this. Wikipedia entry for 'base sets' redirects to Pokemon...

First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined! Okay, let's get to it. I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side...

Homework Statement Simplify the following expression: arccosh \left(\frac{1}{\sqrt{1 - x^2}}\right) \forall x ∈ (-1, 1) Homework Equations cosh(u) = \left(\frac{1}{\sqrt{1 - tanh^{2}u}}\right) u ∈ ℝ The Attempt at a Solution x = tanhu ∴ u = arctanhx u ∈...

Homework Statement find the partial fractions and thus the inverse of the following 6s^2-2s-11/(s-1)(s^2-1) and 7s^2+8s+16/(s+2)(s^2+3) Homework Equations answer tutor gave for the fist one was 3e^2t + 3cosht + sinht and second was 4e^-2t+3cos sqrt3t+ 2/sqrt3 sin sqrt3 The...

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

I understand that given two functions f:X→Y and g:Y→X, to say that f is the inverse function of g means g o f:X→X is defined by g(f(x))=idx and to say g is the inverse function of f means f o g: Y→Y is defined by f(g(x))=idy I understand how to find inverses of one variable functions and...

Homework Statement f(x)=e^x^2 f^(-1)(x)=? 2. The attempt at a solution i reversed x and y so i got x=e^y^2 ln both sides to get lnx=y^2 so (ln(y))^(1/2) what am i doing wrong?

Homework Statement Consider f(\vec{x}) = |\vec{x}|^r, where \vec{x} \in ℝ^n and r \in ℝ. Find \vec{∇}f The Attempt at a Solution I know a vector function maps real numbers to a set of vectors, but here I believe we have the opposite. (inverse of a vector function, assuming inverse...

Hello if y \propto 1/x would 2y \propto 1/0.5x or 2y \propto 1/2x thank you for any replies

I have been struggling to find an inverse to a Lorentz matrix \Lambda using formula: \Lambda^{-1}= \frac{1}{| \Lambda| }\textrm{adj}(\Lambda) from linear algebra. \Lambda = \begin{bmatrix} \gamma&0&0&-\beta \gamma \\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ -\beta \gamma & 0 & 0 & \gamma...

Hello everyone! I'm struggling to find a general formula for obtaining an inverse of a symmetric matrix, for e.g. 1 i -1 i -i 2 -1 2 1 Any help is appreciated!

I'm reading the first chapter of Topology by Munkres. There we can see: "if f is bijective, there exists a function from B to A called the inverse of f . (...) As another situation where care is needed, we note that it is not in general true that f^{-1}(f(A_0) = A_0 and...

I want to perform the inverse of \frac s { [(s+α)^2-β^2](s^2+ω^2)} I know the conventional way is \frac s { [(s+α)^2-β^2](s^2+ω^2)}= \frac{As+B}{[(s+α)^2-β^2]}+\frac{Ds+E}{(s^2+ω^2)} s= (As+B)(s^2+ω^2)+(Ds+E)[(s+α)^2-β^2] \Rightarrow\; A+D=0,\; B+E+2\alpha...

Homework Statement When a camera flashes, the batteries begin recharging the flash capacitor which stores the charge Q according to the function Q(t) = Q* (1-e-t/a) where t is the elapsed time in seconds since the camera flash and Q* and a are non-zero (a) What does Q* represent? (b) Find the...

Homework Statement Let B= \begin{pmatrix} λ-3 & 12 & -1 \\ 0 & λ+2 & λ \\ 0 & 0 & 5 \end{pmatrix} For what values of λ does matrix B have an inverse? Homework Equations The Attempt at a Solution I first tried to calculate det(B)=(λ-3)(5λ+10) +0 -0 to get x=-2 or...

Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?

Homework Statement I need to find the inverse of y=x+√(x^2-1) Homework Equations The Attempt at a Solution I know it's undefined from x=-1 and x=1 so there must be two different inverse functions on two different intervals. I don't know how to find them though.

Homework Statement You know the U substitution proofs for inverse trig functions that go like this: \int\frac{1}{a^{2}+x^{2}}dx \int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx let u = x/a du= dx/a ... \frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...

How to write the algorithm? I figured out a method to find the inverse. The assignment is making use of the property of triangular matrices to find the inverse of a matrix \displaystyle A. The inverse of a triangular matrix(Upper/ Lower) is also triangular(Upper/ Lower) and is easy to find...

Homework Statement The function f(x) has an inverse function, g(x). Find g'(5). Homework Equations f(x) = x^5 + 2x^2 + 2xThe Attempt at a Solution I don't see how I can possibly find the inverse of this function. So I opted to use the derivative rule for inverses. f'(x) = 5x^4 + 4x + 2 5...

Hi, I am taking a random process class and I came across a problem that has stumped me. I believe I know the end result but I would like to know how it is solved. I have been out of college for a while and I am a little rusty with integration. Homework Statement What I need is to find out...

Hello everyone. I am slightly confused by these ideas so i would like your help. How is additive inverse defined? Is unary negation an operation in its own right just like those more familiar, like addition, multiplication? Or something else?

Hi guys, my first post here. This isn't homework or anything, just a personal project. Homework Statement I need to find the inverse of the relative mercator equation. That is, given an origin latitude/longitude, find the current latitude/longitude from an x,y point. Because longitude is...

Homework Statement Let g(x) = (e^x - e^-x)/2. Find g^-1(x) and show (by manual computation) that g(g^-1(x)) = x. Homework Equations g(x) = (e^x - e^-x)/2 The Attempt at a Solution I get the inverse = ln[ (2x + sqrt(4x^2 + 4) ) / 2 ] How do I proceed?

What is the fastest way to find the inverse of a 4x4 matrix? The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.

Homework Statement I'm having problems with finding the inverse equation for this function e^x/(e^x-1) The Attempt at a Solution Currently, I have done about 2 methods to solve it and hitting dead-ends on each one: Attempt 1. x=e^y/(e^y-1) then multiply both sides by (e^y-1) so...

Homework Statement Find the derivative of: 1. f(x)=arccos(5x^3) 2. f(x)=∫cos(5x)sin(5t)dt when the integral is from 0 to x Homework Equations Chain rule, dy/dx=dy/du*du/dx The Attempt at a Solution For the first one, I can just take 5x^3 as u and then apply the chain rule...

maple issue -- inverse laplace transform equation from a basic series RLC circuit Pretty simple for some of you I know, but I have a laplace transform equation from a basic series RLC circuit ((sV-v(0))/L+si(0))/(s^2+sR/L+1/LC) = I(s) I want to take the inverse laplace of it, I am given all...

Homework Statement Homework Equations The Attempt at a Solution for 24. which is a quadratic function, i understand that you have to exchange the positions of x and y and solve from there...but my question is the inverse function of that quadratic for 24 is a negative number...

Homework Statement : Define f: ℝ→ℝ by f(x)=x^2. Find f^-1(T) for each of the following: (a) T = {9} (b) T = [4,9) (c) T = [-4,9] The attempt at a solution: So, the inverse of f should be f^-1(T)=+/-√(x). Therefor: (a) f^-1(9)= +/- 3 (b) f^-1(4)= +/- 2, f^-1(5)= +/- √(5), f^-1(6)= +/- √(6)...

Homework Statement The graph of y=f(x) is shown below. http://Newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data Rank the following from smallest(1) to largest(4). f−1(0) f(0) f(5) f−1(5) Homework Equations none available The...

Here is my problem: cot(arcsin(x)) my awnser: cot= x/(1-x)^1/2 The online program were suppose to use says I am wrong but I am not sure what I did wrong.

Evaluate the integral \int \frac{x}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, dx by making the substitution u = x^{2}Homework EquationsThe Attempt at a Solutionu = x^{2} - 4 so \frac{du}{2}= xdx \int \frac{1}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, xdx \frac{1}{2} \int \frac{1}{(u) \sqrt{x^4 - 8x^2}} \...

Homework Statement The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and...

Hello PF! I've got a strange question for you physics boffins; assuming for a moment that lasers obeyed the inverse square law, what range would a typical 1mW red laser have in the atmosphere?

Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...

Homework Statement Given y = 2/3(arctan \frac{x}{4}), find x. Homework Equations Inverse trigonometric identities for tan. (I guess)The Attempt at a Solution I never attempted because it seems impossible for me. You think this is possible? Thank you!

EDIT: 1.Homework Statement The problem asks to simplify this: cos(arcsin x)Homework Equations let arc sin x = θThe Attempt at a Solution EDIT: I have to edit because I received a warning for not posting for #3 and #2. I originally posted "cos(arcsin x)" for #2 because that was what I know...

Homework Statement Find the inverse of a rational function: f(x)=\frac{2x}{x-2} The Attempt at a Solution 1. Verify the function is one-to-one. Question: is there a way to do that withought drawing the graph? Some algebraic method? I know that this means that the function crosess any given...

Consider the function f: R-->R where F(x)= x, if x<1 x², if 1<x<9 (read x <or equal to 1 and x< or equal to 9) 27*sqrt(x), if x>9 I know that f is not differentiable at x=1 and x=9 because the derivative at each one of these points don't exist once the lateral limits don't coincide.(Is...

Homework Statement How do I find out the exact value of tan^-1 (1 / sqrt(3))? Homework Equations nada The Attempt at a Solution I don't know where to start.