Inverse Definition and 1000 Threads

Hello! *Let $f$ be a strictly increasing continuous function on a closed interval $[a, b]$, let $c = f(a), d = f(b)$, and let $g:[c, d] → [a, b]$ be its inverse. Then $g$ is a strictly increasing continuous function on $[c, d]$.* How can it be shown that $g$ is continuous at its endpoints $c$...

Homework Statement Find the inverse of the function: Y=X2-X, X≥½ Homework EquationsThe Attempt at a Solution I've switched X and Y to get: X=Y2-Y Then I've tried several things to get Y alone, but none of them seem to work. I've tried taking a square root, using a log, and several other...

I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...

I know for two linear operators $$H_1, H_2$$ between finite dimensional spaces (matrices) we have the relations (assuming their adjoints/inverses exist): $$(H_1 H_2)^* = H_2^* H_1^*$$ and $$(H_1 H_2)^{-1} = H_2^{-1} H_1^{-1}$$ but does this extend to operators in infinite dimensions? Thanks.

I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's proof of the Inverse Function Theorem (IFT) for real-valued functions of one real variable. Stoll's statement of the IFT for Derivatives and its proof read as follows: In the above proof we read: "...

Scaling - Inverse relationship between uncertainty and mass I’m trying to express Heisenberg's Uncertainty Principle in a simplified formula that is not boundary unlimited and still capture what I believe is an inverse relationship between uncertainty and mass - the "scaling hypothesis". I...

Homework Statement find the inverse of r in R = F[x]/<h>. r = 1 + t - t^2 F = Z_7 (integers modulo 7), h = x^3 + x^2 -1 Homework Equations None The Attempt at a Solution The polynomial on bottom is of degree 3, so R will look like: R = {a + bt + ct^2 | a,b,c are elements of z_7 and x^3 = 1 -...

Homework Statement arccot x = (π/2) - arctan x arccot x =/= π arccot x =/= 0 Homework Equations arccot x = 1/arctan x (if x > 0) arccot x = 1/arctan x + π (if x < 0) arccot x = π/2 (if x = 0) The Attempt at a Solution π and 0 are the horizontal asymptotes, the values for which y (sine) cannot...

Homework Statement Calculate the total number of compex multiplications required for the calculation in (b) when FFTs are used to perform the Discrete Fourier Transforms and Inverse Discrete Fourier Transforms.[/B] There were two FFT multiplied together and one inverse FFT of that product to...

One semester I was asked to find the inverse of $\,f(x) \:=\:\dfrac{3x - 5}{2x+1}$ Later, I had to find the inverse of $\,f(x) \:=\:\dfrac{2x+7}{4x-3}$ It occurred to me that a general formula would a handy tool. Especially since I planned to teach Mathematics and I might be teaching this very...

What is higher inverse orders of n, as symbolized by O(n)? Please explain this to me---I am still confused even if googling it.

Homework Statement Don't understand why the inverse jacobian has the form that it does. Homework Equations $$ J = \begin{pmatrix} \frac{\partial{x}}{\partial{u}} & \frac{\partial{y}}{\partial{u}} \\ \frac{\partial{x}}{\partial{v}} & \frac{\partial{y}}{\partial{v}} \end{pmatrix} $$ $$...

Homework Statement Hi! Does anyone know how to solve the inverse of these functions? y=(4x^2+2x-2)/(8x^2-4x+6) y=(x+1)/(x^2) I would appreciate your help with these exercises. The Attempt at a Solution For the first one: 8yx^2-4xy+6y=4x^2+2x-2 For the second exercise: yx^2=x+1 yx^2-x=1

f(x) = 3x^3 + 3x^2+ 2x + 1 ,a = 3 formal is Homework is due tonight and this is the only problem i can't solve Your suppose to 3= 3x^3 + 3x^2 + 2x + 1 , solve for xThe find the derivative of y= 3x^3 + 3x^2 + 2x + 1 , then plug x into that and put it under 1.

Hi guys! I am having a problem in finding the inverse z transform of the given signal. Can anyone help me? I'd appreciate it. Thanks! Here is basically what I did: However, I don't know what to do next. What is the next thing to do? Thanks!

Homework Statement If we shift a curve to the left, what happens to its reflection in the line y = x? In view of this geometric principle, find an expression for the inverse of g(x) = f(x + c) where f is a one-to-one function. Homework EquationsThe Attempt at a Solution Initially I did this...

Hello! (Happy) In my lecture notes, there is this remark: A set $X$ is countable iff there is a $f:X \overset{\text{bijective}}{\longrightarrow} \omega$ iff $X$ is the range of a bijective sequence of lengh $\omega$. $$f^{-1}: \omega \overset{\text{bijective}}{\longrightarrow} X$$ then...

Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? & If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I...

Homework Statement Dear Mentors and PF helpers, Please help me with this question as my junior asked me but I have some doubts in it: It takes 4 workers to complete repairing the road in 42 days. Suppose that 14 days into the road works, 10 more workers are brought into help out in the road...

Hey! :o Does it stand that the eigenvalues of $A^{-T}A^{-1}$ are the inverse of the eigenvalues of $A^TA$ ?? (Wondering)

Hi, let's say in some experiment with ##Z^0## (eg LEP) you are able to determine the "misidentification" of your particles. Then you can find the efficiency matrix ##M_{eff}## which is given (for ##Z^0## decays to leptons or hadrons): \begin{pmatrix} N_e \\ N_\mu \\ N_\tau \\ N_{had}...

Homework Statement Give the inverse Laplace transform of F(s) = (-3/s) + (e^-4s)/(s^2) + (3e^-4s)/s Homework Equations Inverse Laplace [e^(-cs) F(s)] = f(x-c)u(x-c) The Attempt at a Solution I'll break this into 3 parts. Part 1 - (-3/s) -3/s = -3(1/s) -> inverse laplace of -3(1/s) = -3...

Homework Statement This comes up in the context of Poisson's equation Solve for ##\mathbf{x} \in \mathbb{R}^n ## $$ \nabla^2 G(\mathbf{x}) = \delta(\mathbf{x})$$ Homework Equations $$\int_0^\pi \sin\theta e^{ikr \cos\theta}\mathop{dk} = \int_{-1}^1 e^{ikr \cos\theta}\mathop{d\cos \theta }$$...

Assuming that my understanding is correct, I believe it was Einstein who proposed that gravity is the result of the warping or curving of space-time. My question is this: if gravity, which is solely attractive in nature, is the result of warped or curved space time, then is it possible for the...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Homework Statement find the inverse laplace Homework Equations L^(-1)[(s+1)^2/(s+2)^4] The Attempt at a Solution included in attachment. the top problem, #20.

Homework Statement Let ##f : G \rightarrow H## be an epimorphism from a group ##G## to ##H## and let ##h \in H##, then ##f^{-1} (h) = g ~ker(f)##. Homework EquationsThe Attempt at a Solution So, if I understand the problem correctly, we are trying to find a epimorphism which has a rule such...

Inverse Laplace transform \mathcal{L}^{-1}[F(p)]=\frac{1}{2\pi i}\int^{c+i\infty}_{c-i\infty}F(s)e^{st}dp=f(t) Question if we integrate along a straight line in complex plane where axis are Re(p), Im(p), why we integrate from c-i \ínfty to c+\infty? So my question is, because Im(p) are also...

Homework Statement Find the inverse Fourier transform of X(ejw = 1/(1-ae-jw)2 using the convolution theorem. Homework EquationsThe Attempt at a Solution I tried finding the partial fraction coefficients but without success.

Hello, everybody. I am currently working on deriving solutions for Stokes flows. I encounter a multidimensional inverse Fourier transform. I already known the Fourier transform of the pressure field: \tilde{p}=-\frac{i}{{{k}^{2}}}\mathbf{F}\centerdot \mathbf{k} where i is the imaginary unit...

Homework Statement Division by s Equals integration by t: For this problem use the following property (see relevant equations) to find the inverse transform of the given function: F(s) = \frac{1}{s(s-1)} Homework Equations L^{-1}(\frac{F(s)}{s}) = \int_{0}^{t} f(\tau)\,d \tau The Attempt...

Hi! (Wave) Could you give me a hint how I could show that if $f$ is a function, that is $1-1$, then, it stands that: $$(\forall x \in dom(f)) f^{-1}(f(x))=x$$ ? (Thinking)

Homework Statement Hi there! I have a data set of r (independent variable) and E (electric field strength) (dependent variable). The question asks for a non graphical method to show if there is an inverse square law relationship between the two data sets. -- My attempt: I picked the equation...

Hi all What if instead of charges and a surface, we were given a set of charges and image charges and have to find the surface, how would you do that? This is actually part of my homework but I'm pretty sure he doesn't want us to prove it mathematically (the case is obviously a sphere) so I...

Homework Statement ...(2 , 3) A = ...(1 , 3) Find the trace of A^(-1) Homework Equations (a , b)......(d , -b) ...^(-1) = (ad-bc)^(-1)* (c , d).......(-c, a) The Attempt at a Solution .....(3 , -3) A^-1 = 9* .....(-1. 2) (In mod 26) ... (1, -1) = ... (-9...

Why exactly is there no such thing as an inverse factorial function? Now I am fully aware of the fact that the factorial function (##f(x) = x!##) is not one-to-one, since both 0! and 1! equal 1. But can't we circumvent this by restricting the domain of f such that it only includes values of x...

I seem to recall reading a geometry method that showed zero to be the inverse of infinity. Can you give me a reference for that?

After working a homework assignment which required sketching effective potential energy for the gravitational/coloumb forces, I went and looked at a few effective potentials for inverse cube and inverse quartic (not sure if this is the right word; 1/r^4 force) forces, with inverse square and...

Homework Statement Determine which of the formulas hold for all invertible nhttp://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmsy10/alpha/144/char02.png n matrices A andB A. 7A is invertible B. ABA^−1=B C. A+B is invertible D. (A+B)2=A2+B2+2AB E. (A+A^−1)^8=A8+A−8 F...

Homework Statement the problem is to find the inverse of a 3x3 matrix using LU Decomposition with C++ command, with the numbers designated. in my case, my numbers for the matrix are '306 410 780' #include <stdio.h> #include <iostream> #include <stdlib.h> #include <math.h> using namespace std...

<< Moderator Note -- thread moved to the Homework Help forums >>[/color] I'm stuck on a problem, and I'm in serious need of help. I) Problem: Find the solution to f (t) = 2 \int^t_0 f'(u) sin 3 (t-u) \ du + 2 cos (3t) . Also find f (0) .II) Solution, so far: F(s) = 2 (s F(s) - f(0)) *...

Hello everyone, I have spend whole day but still not figure out an inverse Laplace transform. Hope someone can help me. The question is in the attachment. I'm trying to extract u^2/4D^2 out the bracket to match the standard inverse table, but it seems difficult to deal with the square root...

Homework Statement Verify that f has an inverse <- prof told us not to worry about this. Then use the function f and the given real number a to find (f^-1)'(a). f(x) = Cos(2x), 0<=x<=pi/2 where a=1 Homework Equations 1/(f'(g(x))) where g(x)=f^-1(a) d/dx(cos(2x)) = -2sin(2x) The Attempt at a...

Homework Statement Hello! Please, take a look at the attached picture - there is a quote of the exercise and below is my attempt to make a matrix. Is my matrix correct? I have tried many times to convert it to inverse one, but I can't figure out how to do it - I keep getting "inconvenient"...

The normal answer is "no, there is no inverse function in terms of the normal operators and trigonometric functions." That is to say, given a value of x, you cannot find the value of y of the input function reflected over the x-y axis using standard functions. "Standard functions" is what is...

Hi...can anyone please suggest whether the following inverse has a power series expansion (I+\delta A)^{-1} where \delta is a constant and A = \begin{pmatrix} T & T-1 & T-2 &... & 3 & 2 & 1\\ T-1 & T-1 & T-2 & ... & 3 & 2 & 1 \\ .. \\2 & 2 & 2 &... & 2 & 2 & 1 \\ 1 & 1 & 1 & ... & 1 & 1 & 1...

Hello, While studying dual vectors in general relativity, it was written as we all know that dual vectors (under Lorentz Transformation) transform as follows: \tilde{u}_{a} = \Lambda^{b}_{a}μ_{b} where \Lambda^{b}_{a}= η_{ac}L^{c}_{d}η^{db} I was wondering if one can prove the latter...

So in beta decay I know a neutron can decay into, proton, electron and antineutrino (Or, neutrino, since they're both the same?) But anyhow, regardless of the neutrino, in neutron stars electron degeneracy doesn't hold and electrons combine with photons to form neutrons. But isn't that...

Homework Statement Decide the inverse laplace transform of the problem below: F(s)= \frac{4s-5}{s^2-4s+8} You're allowed to use s shifting. Homework Equations The Attempt at a Solution By looking at the denominator, I see that it might be factorized easily, so I try that...