Inverse Definition and 1000 Threads

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 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...

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...

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.

\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}+...

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...

Homework Statement B=magnetic flux density . A is the vector potential of magnetic field. How to get the formula B=∇A Homework Equations http://en.wikipedia.org/wiki/Magnetic_moment The Attempt at a Solution B=magnetic flux density . A is the vector potential of magnetic field...

Hello, The inverse square law of Newton's gravitational force, is it somehow related to each other? I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived? Thanks.

Homework Statement Find the inverse of AB if A^(-1)= [4,0;-2,2] and B^(-1)=[-2,0;-2,3]. (See below for picture/additional information.)Homework Equations Inverse of AB = inverse of A*inverse of B The Attempt at a Solution Using above equation: (AB)^(-1) = [4,0;-2,2]*[-2,0;-2,3] =...

I am trying to solve the following problem on an old Quantum Mechanics exam as an exercise. Homework Statement Homework Equations I know that the trace of an operator is the integral of its kernel. \begin{equation} Tr[K(x,y)] = \int K(x,x) dx \end{equation} The Attempt at a...

Homework Statement compute the inverse derivative of f(x) = x^3/(x^2+1)Homework Equations n/aThe Attempt at a Solution My issue is a purely algebraic one... getting the inverse function! Attempting to solve for x yields no results! y = x^3/(x^2+1) y(x^2+1) = x^3 yx^2 + y = x^3 y = x^3 - yx^2 y...

Hi, I need to rearrange an equation: y = ax^2 + bx + c to the form of: x = ? I'm not entirely sure how to go about this and the examples I've found require the equation to be in a different form. Any tips or a point in the right direction would be great! Thanks in advance

Hi! I'm struggling with the bellow truth tables: P = I live in Paris Q = I live in France A B C P → Q Q → P ¬ Q → ¬ P S S S S S S F S F S F F F S S S F F F S S S F F F S S F S F F S F S S S Table A and C I'm...

Hi all, I have a ground excited single degree of freedom model, like that: http://www.bsw-schwingungstechnik.de/fileadmin/user_upload/images/2/graphic-passiv-isolation.jpg I know the excitation function, i.e. s(t), but I need to know the force that imposes a specific s(t). I need it...

Homework Statement I have a general question about light and Lumens and the inverse square law? So Intensity = Initial Lumens/Lenth^2 So @ a Length of 1, there is no loss of light intensity. What unit is this 1. 1 meter? 1 foot? Homework Equations The Attempt at a...

inverse square vs cube = ? If the electric field falls off at the inverse square ratio, and magnetic at inverse cube, does EM radiation dissipate at 1/r^5 ratio for circularly polarized waves?

Dear all, I am reading R.A. Sharipov's Quick Introduction to Tensor Analysis, and I am stuck on the following issue, on pages 38-39. The text is freely available here: http://arxiv.org/abs/math/0403252. If my understanding is correct, then the Jacobi matrices for the direct and inverse...

\Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\omega t+\delta)}\right) I want to find out whether ##\Psi## increase or decrease with time t, if ##\delta## is positive and if ##\delta## is negative. \Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\cos\omega t \cos \delta+\sin\omega t...

Homework Statement Let A be a square matrix. a. Show that (I-A)^-1 = I + A + A^2 + A^3 if A^4 = 0. b. Show that (I-A)^-1 = I + A + A^2 + ... + A^n if A^(n+1) = 0. Homework Equations n/a The Attempt at a Solution I thought I'd want to use the fact that the multiplication of a...

I must fundamentally misunderstand what the variational method is. According to my textbook, it's used to find the minimum eigen energy of an operator (in particular, the time-independent schrodinger equation). This appears to be synonymous to finding the eigenvalues of the matrix representation...

Here is the question: Here is a link to the question: Given 0<x<orequalto 1, determine the value of inversine (x) + inversetan (squareroot(1-x^2)/x)? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

Here is the question: Here is a link to the question: A math function question please help? - Yahoo! Answers I have posted a link there to this topic so that the OP may find my response.

Homework Statement how do I solve this question https://www.dropbox.com/s/bn958xnm5483s6u/photo%20%281%29.JPG (This link if the image is not visible : https://www.dropbox.com/s/bn958xnm5483s6u/photo%20%281%29.JPG) just so the equation is not clear it says A2 = λA - 2I The inverse should be...

This is very tricky for me. How to find the inverse laplace of 1s. I haven't been taught the integral method of inverse. Only the formula based , splitting terms kind of thing. I used MATLAB and found it was dirac delta. But how do I get to it without using the integral for inverse?

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Reaaly need to solve these

Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} Homework EquationsThe Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting (...

Homework Statement Could anyone please check my work, The answer is wrong. Correct Answer: e^2t(-t+e^t-1) Homework Equations Inverse Laplace The Attempt at a Solution Here's my solution, please point out my mistakes. One mistake i found after taking the picture is: Its -2te^-2t ( third...

In Topology: is the multiplicative inverse of a metric, a metric? How do we define the Schwarz inequality then? if ##d(x,z) ≤ d(x,y) + d(y,z)## the inverse ##1/d(x,z)## would give the opposite?