Inverse Definition and 1000 Threads

Homework Statement tan-1[2x/(1-x2)]+cot-1[(1-x2)/2x]=2π/3 2. The attempt at a solution tan-1[2x/(1-x2)]+cot-1[(1-x2)/2x]=2π/3 tan-1[2x/(1-x2)]=2π/6 take tan on both sides 2x/(1-x2) =sqrt(3) quadratic equation so it should have 2 solutions(sqrt(3) and sqrt(1/3)).But this question...

Hey everyone. Sorry to post another topic, but i thought this would be easy to find on google, to help me with , but i can't find it. All I am really lookin for is someone to let me know if my answers are right, and if not, then how i can fix them :) Anyways, i was asked to graph...

f(x) \ = \ \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}Edit: \ \ I \ sent \ a \ PM \ to \ a \ mentor.

IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform Homework Statement Solve x"+x'+x=1, given x(0)=x'(0)=0 Homework Equations The Attempt at a Solution Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s Plugged in initial value points, simplified...

Homework Statement Hello all, Having difficulty with this one question that involves complex roots. Here it is: F(s)=\frac{s+3}{s^3+3s^2+6s+4} I tried two different ways to tackle it. First method I divided it right away: F(s)=\frac{s+3}{s^3+3s^2+6s+4}\rightarrow{s^2+6-\frac{14}{s+3}} Is there...

Why are Newtons law of universal gravitation, F=G\frac{m_{1}m_{2}}{r^{2}} and Coulombs law, F = K_{e}\frac{q_{1}q_{2}}{r^{2}} inverse square laws? I understand why they are inverse because the force decreases with distance but why is the distance, r, squared? Thanks AL

I feel kind of lame, but here's my situation: We start with the operator g_{\mu \nu} \Box - \partial_{\mu}\partial_{\nu} and convert to momentum space to get -g_{\mu \nu} k^{2} - k_{\mu}k_{\nu}. Apparently it's easy to see that this has no inverse? I'm told that if it *did* it would be...

I am reading the proof of the Inverse Function Theorem in baby Rudin and I have a question about it. How does associating a function phi(x) (equation 48) with each point y tell us anything about if f(x) is one-to-one? I'll show the proof below. Also, if f'(a) = A, and f(x)=x2, what would A-1 be?

Homework Statement find the derivative of the function f(x)=arcsec(4x) Homework Equations I think this is a Relevant equations. d/dx[arcsecu]=u'/(|u|(√u2-1) The Attempt at a Solution f'(x)=4/(|4|(√42-1) =1/√15 I keep getting wrong in my online homework why? :confused:

Homework Statement arctan(8x-8)=-1 Homework Equations I'm sure what this part wants. The Attempt at a Solution tan[arctan(8x-8)]=tan(-1) 8x-8=tan(-1) x=(1/8)(tan(-1)+8) x=(1/8)(-(tan(1)+8) x= I am stuck on the last part since the homework says Simplify the above equation...

Homework Statement Find the derivative of the compositional inverse of f(x) = sin(1/x) restricted to (1,∞). You may use without proof that sin(x) is differentiable with derivative cos(x). Homework Equations (f^{-1})'(y_0) = \frac{1}{f'(f^{-1}(y_0))} The Attempt at a Solution...

Homework Statement Find (f^{-1})'(a) of: f(x)=\sqrt{x^{3}+x^{2}+x+22} ; a=5. Homework Equations (f^{-1})'(a)=\frac{1}{f'((f^{-1})(a))} The Attempt at a Solution Well, I know to find an inverse: I need to set the equation equal to y, solve for x, then swap x and y. But I don't...

Homework Statement The function f:x→ 4-x2 for the domain x≤0. Find the inverse of is denoted by f-1 and state the domain and range of f-1. Homework Equations Set equation to 0 and solve for x to find inverse. The D and R is going to be switched for the inverse..? The Attempt at a...

I am having problem with the inverse transformation of a Fourier transformed function which should give the function itself. Let f=f(x) and let f be Fourier transformable (whatever that implies) Let \tilde{f}(k)=∫^{\infty}_{-\infty}dx e^{-ikx}f(x) (1) then we should have...

Homework Statement For α > 0, determine u(x) by the inverse Fourier transform u(x) = \frac{1}{2\pi}\int_{-\infty}^{\infty}\ \frac{e^{ikx}}{ik+\alpha}\ dk Homework Equations The Attempt at a Solution This seemed like a relatively simple residue problem. You just note that...

Homework Statement [SIZE="7"]∫ (x+2)dx/√(4x-x2) Homework Equations why was the -2 in -2(x-2) was ignored? The Attempt at a Solution so first i let u= 4x-x2 then, du=4-2x = -2(x-2) so to get (x+2) i equate it to (x-2)+4 so ... [SIZE="7"]∫ (x+2)dx/√(4x-x2) =...

This is insane, I am trying to revise the inverse of matrices and this one element is being really stubborn, please help. Here is the matrix 3 -1 7 2 0 1 5 -2 6 I have transposed it 3 2 5 -1 0 -2 7 1 6 Now as for replacing the element of...

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 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...

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...