Inverse Definition and 1000 Threads

Homework Statement Can an inverse function be determined as either even or odd simply given its original function?

Homework Statement Let S={p+qα+rα2 : p, q, r \in \mathbb{Q}}, where α=\sqrt[3]{2}. Then S is a subfield of \mathbb{C}. Prove that each nonzero element of S has a multiplicative inverse in S. The Attempt at a Solution Let p, q, r\in\mathbb{Q} such that not all of p, q, r are zero. If...

Homework Statement Find the inverse Laplace transform of the expression: F(S) = \frac{3s+5}{s^2 +9} Homework Equations The Attempt at a Solution From general Laplace transforms, I see a pattern with laplace transforming sin(t) and cos(t) because: L{sin(t)+cos(t)} =...

Homework Statement Find the formula of the inverse function of f(x)=300/(3+15e^.05x). Homework Equations f(x)=300/(3+15e^.05x) The Attempt at a Solution I'm definitely way off but I got .05y(5x)+ln100=lnx. What I did was multiple the denominator by the y(cross mltiplication)...

Hi, I have a relationship $$P \cong \Bigg[\Big(K_1\rho^{\frac{5}{3}}\Big)^{-2}+ \Big(K_2\rho^{\frac{4}{3}}\Big)^{-2}\Bigg]^{-\frac{1}{2}}$$I need to find the inverse as $$\rho= \rho(P)$$. I made a detailed calculation and came up to this $$y^5+\Big(\frac{P}{K_2}\Big)^2 y+...

Dear friends, I have been trying in vain for a long time to understand the proof given in Kolmogorov and Fomin's of Banach's theorem of the inverse operator. At p. 230 it is said that M_N is dense in P_0 because M_n is dense in P. I am only able to see the proof that (P\cap M_n)-y_0 \subset...

Consider the function g(x) represented by the table below: x -6 -4 -2 0 2 4 6 g(x) -4 -2 4 0 6 -6 2 Complete the table of values for the INVERSE, g^{-1}(x), in the table below: x -6 -4 -2 0 2 4 6 g^{-1}(x)

Hello. Nice to meet you. I have just enrolled. :) I knew how to solve and to find out inverse Matrix by using Gaussian elimination. However, I was wondering why AI -> IA' is satisfactory. In my university, I was just taught how to use but wasn't taught why it is satisfactory. Thank you for...

Homework Statement Consider the Schwarschield Metric in four dimensional spacetime (M is a constant): ds2 = -(1-(2M/r))dt2 + dr2/(1-(2M/r)) + r2(dθ2 + sin2(θ)dø2) a.) Write down the non zero components of the metric tensor, and find the inverse metric tensor. b.) find all the...

Homework Statement A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position. Homework Equations B+A/x^2=m*a...

I've always been having trouble with the domain and range of inverse trigonometric functions. For example, let's start with an easy one: $\sin^{-1}\left({x}\right)$ Process: First, I draw out the function of $\sin\left({x}\right)$. Then I look at its range and attempt to restrict it so that it...

Homework Statement Fin the value of arccot(pi/4) Homework Equations unit circle The Attempt at a Solution I honestly can't believe that I'm stuck on this as this shouldn't stump me. My logic is that since its inverse cotangent then its related to inverse tangent and so the...

Homework Statement For the following dimensional equation, find the base dimensions of the parameter f: M M-3 = a cos( f L ) Homework Equations M represents mass, a represents acceleration due to gravity, in terms of mass * length over seconds squared [[M * L]/[t2]] where L represents length...

Hi all looking for a bit of advice me the misses and the kids are starting a indoor flower garden and some herbs for the kids now my problems have come down to the lighting I have found out the colour spectrums needed as well as the luminous intensity required for heathly plant growth but the...

Reference to Griffith electrodynamics question:- 1.16 Compute the divergence of an inverse square vector field. Now gradient is (∂/∂r)(r cap) Hence upon taking divergence of inverse square field (r cap)/r^2...We don't get 0. In fact we get (-2)/r^3. But if we write the vector field and...

Hello all, I have a matrix A: \[\begin{pmatrix} 2 &4 &1 \\ -4 &7 &3 \\ 5 &1 &-2 \end{pmatrix}\] and I need to find the adjoint of the matrix inverse. I found adj(A) to be: \[\begin{pmatrix} -17 &9 &5 \\ 7 &-9 &-10 \\ -39 &18 &30 \end{pmatrix}\] and I found the determinant of A to be -45 and...

Find an integer $k$ for which $\dfrac{1}{k}+\dfrac{1}{k+1}+\dfrac{1}{k+2}+\cdots+\dfrac{1}{k^2}>2000$.

Homework Statement Hi. I need help to resolve the inverse laplace transform of {1/((x^2)+1)^2}2. The attempt at a solution I have tried to do: {(1/((x^2)+1) * (1/((x^2)+1)} then, convolution, sen x But, isn't working Thanks for your help :)

Homework Statement Find inverse z-transform of X(z) = \frac{z}{(z-0.2)^2(z+0.1)} Homework Equations The Attempt at a Solution : partial fraction My method :\frac{X(z)}{z} = \frac{1}{(z-0.2)^2(z+0.1)} \frac{X(z)}{z} = \frac{-100/9}{(z-0.2)} + \frac{10/3}{(z-0.2)^2} + \frac{100/9}{z+0.1} X(z) =...

Hey guys, I have a couple of questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For 1a, using inverse trigonometric derivative identities should work, right? I got y' = 1/sinØ + 1/cosØ and multiplied by the common...

Hey guys, I've a few more questions this time around from my problem set: (Ignore question 2abc, I only need help with the first one) Question: For the first one, in order to prove that a function is one-to-one, f(x1) =/ f(x2) when x1 =/ x2. Thus, the horizontal test applies. So I said...

Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: Alright, I'm having quite a bit of trouble with these. So here it goes: For the first one, I did the 3-step procedure to finding the...

Homework Statement Show that the given function is a cdf (cumulative distribution function) and find F_X^{-1}(y) (c) F_X(x) = \frac {e^{x}}4 , if x<0, and 1-(\frac {e^{-x}}4) , if x \geq 0 Homework Equations for a strictly increasing cdf, F_X^{-1}(y) = x \iff F_X(x) = y and for a...

Homework Statement Ds + E / (s^2 +1)^2 Homework Equations The Attempt at a Solution Ds / (s^2 +1) + E / (s^2 +1) D[s/(s^2 + 1)^2] + E [1 / (s^2 + 1)^2]

before I go to bed(it's 11:30pm in my place), here is the last problem that I need help with find the inverse Laplace Transform $\frac{4s-2}{s^2-6s+18}$ the denominator is a non-factorable quadratic. I don't know what to do. thanks!

find the inverse Laplace of the ff: 1. $\frac{n\pi L}{L^2s^2+n^2 \pi^{2}}$ 2. $\frac{18s-12}{9s^2-1}$ for the 2nd prob I did partial fractions $\frac{18s-12}{9s^2-1}=\frac{9}{3s+1}-\frac{3}{3s-1}$ $\mathscr{L}^{-1}\{\frac{18s-12}{9s^2-1}\} =...

Hello all, If Planck length (1.61619926 × 10(-35 )meters) places a theoretical limit on minimum possible distance does it also imply that we have a maximum theoretical limit on measurable length as inverse of Planck length (1/Planck Length).. does there any such limit on the maximum...

Homework Statement What is the inverse of the 3x3 matrix mod 26? K = \begin{pmatrix} 17 & 17 & 5\\ 21 & 18 & 21\\ 2 & 2 & 19 \end{pmatrix} Homework Equations The Attempt at a Solution So I found all the cofactors and then took the transpose of the matrix. I then...

Homework Statement \begin{pmatrix} 5 & 8\\ 17 & 3\\ \end{pmatrix} The matrix given above is matrix A and I am trying to find A-1 mod 26 = ?Homework Equations ax+by = cThe Attempt at a Solution Well first I found the det of A which is -121 and then took -121 modulus of 26 which gave me 9. Did...

I just started Calculus 1, a summer quarter that's compressed and I'm having trouble understanding a theorem that state continuity of the inverse function. Within my textbook, it mentions "If f(x) is continuous on an interval I with range R, and if inverse f(x) exists, then the inverse f(x) is...

Homework Statement in mod 35, find the inverse of 13 and use it to solve 13x = 9 gcd(35,13) =1 so the inverse exsists: 35 = 2*13 + 9 13 = 1*9 + 4 9 = 2*4 + 1 4 = 4*1 and then to find the linear combination 1 = 9 - (2*4) = 9 - 2(13-9) = 3*9 - 2*13 = 3* (35 - 2*13) - 2*13 = 3*35 - 8*13 =...

Show that if A, B and A+B are invertible matrices with the same size, then $$A(A^{-1}+B^{-1})B(A+B)^{-1}=I$$ What does the result in the first part tell you about the matrix $$(A^{-1}+B^{-1})$$? I get the first part. Help me with the second part. My book says that the matrix...

If ##V_{BA} = P_B - P_A## (where V is the voltage and P the potential) so, ##V_{AB} = - V_{BA}##. The same ideia for the current: ##i_{BA} = - i_{AB}##, so this ideia of sense is true too for resistor, inductor and capacitor? The resistance, inductance and capacitance of an arbitrary sense is...

I think this looks like a homework problem, so I'll just put it here. Homework Statement Demonstrate that, for any index category ##\mathscr{J}## and any diagram ##\mathcal{F}:\mathscr{J}\to\mathbf{Sets}##, $$\varprojlim_{\mathscr{J}}A_j=\left\{a\in \prod_{j\in \operatorname{obj}(...

Hello all, I have say 512-by-512 matrix, but based on the structure of this matrix most elements not on the diagonals between -5 to +5 (- stand for diagonal below the main diagonal, and + for diagonal above the main diagonal) are small relative to the elements of the mentioned diagonals. So...

How can we prove $$\displaystyle \tan^{-1}\left(\frac{4}{7}\right)+\tan^{-1}\left(\frac{4}{19}\right)+\tan^{-1}\left(\frac{4}{39}\right)+\tan^{-1}\left(\frac{4}{67}\right)+...\infty = \frac{\pi}{4}+\cot^{-1}(3)$$ My Trial: First we will calculate $\bf{n^{th}}$ terms of Given Series...

Homework Statement \int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dkHomework Equations The Attempt at a Solution As you can guess, this is the inverse Fourier transform of |k|^{2\lambda}. I've tried splitting it from -infinity to 0 and 0 to infinity. I've tried noting that |k| is even, cos is...

Homework Statement I have a function f:M_{n×n} \to M_{n×n} / f(X) = X^2. The questions Is valid the inverse function theorem for the identity matrix? It talks about the Jacobian at the identity, but I have no idea how get a Jacobian of that function. Can I see the matrices as vectors and...

Hi there! I'm back again with functions over matrices. I have a function f : M_{n\times n} \to M_{n\times n} / f(X) = X^2. Is valid the inverse function theorem for the Id matrix? It talks about the Jacobian at the Id, but I have no idea how get a Jacobian of that function. Can I see that...

By considering the product of complex numbers: $$z = (2+i)(3+i)$$ Show that $$\tan^{-1}\frac{1}{2} + \tan^{-1}\frac{1}{3} = \frac{\pi}{4}$$

Hey guys. In a project I'm working on, it would be very convienent to express the inverse of this matrix in terms of its size, NxN. The matrix is \leftbrace \begin{tabular}{c c c c} a & b & \ldots & b \\ b & a & \ldots & b \\ b & b & \ddots & b \\ \vdots & vdots & ldots & b \\ b...

Homework Statement f(s) = 6/s^2-9 Homework Equations I think f(t) = (1/b-a)(e^-at-e^-bt) The Attempt at a Solution Replace 6/s^2-9 with 6/(s-3)(s+3) a=-3 b=3 Plug in (1(6)/3-(-3))(e^-(-3)t-e^-3t) Final Result e^3t-e^-3t

Homework Statement f(s) = -5s/S^2+9 Homework Equations I think f(t) cosωt = f(s) s/s^2+ω^2 The Attempt at a Solution ω=3 Answer -5cos(3t) Can anyone tell me if I did this correctly? I think I did but just want to make sure, if not can you tell me what I did wrong? Thanks

Solve the following system of equations using the inverse of the coefficient matrix, 2x + 4y = -9 -x - y = 2 My attempt- [2 4 [x = -9 -1 -1] y] = 2 |A| x b |A| = -2-4=-6 [x = 1/-6 [-1 -4 [-9 1/-6 [ 1 = 0.03 y] = 1...

When thinking of a spherical shaped particle moving about under Brownian motion, one describes its motion by Diffusion. The units being \frac{m^2}{s} I can understand this physically as a distance it will travel from a certain point in space averaged over x-y and z direction. Now rotational...

Hi everyone, :) An interesting question I thought about recently. Is it true that a Latin Square of integers (or real numbers) treated as a matrix is always invertible? If not can anybody give a counterexample. I think latin squares are invertible but I am unable to prove it. Hope you can help...

Hello, This is the thread I originally wanted to respond to, but it's closed: https://www.physicsforums.com/showthread.php?t=650126 I also found this on Wiki-talk page, which seems to be the same argument...

Homework Statement This was in my test paper today: A transformer is cut into half so that one half contains the primary coil and the other half contains the secondary coil. They are moved 30cm apart. Explain why the transformer would not work The Attempt at a Solution My answer: The magnetic...

Homework Statement Problem One: Two kilometres away from a point source of infrared waves, the intensity is 4 Mw−2. Calculate the intensity 1m away from the source. Problem two: Light from a candle has an intensity of 20.0 units when a meter is placed 3.0m away. What is the reading on the...

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.