Inverse Definition and 1000 Threads

To prove that $$sin^{-1}(ix)=2n\pi\pm i log(\sqrt{1+x^2}+x)$$ I can prove $$sin^{-1}(ix)=2n\pi+ i log(\sqrt{1+x^2}+x)$$ but facing problem to prove $$sin^{-1}(ix)=2n\pi- i log(\sqrt{1+x^2}+x)$$ Help please

Homework Statement Is there a way to evaluate L^{-1}(\frac{F(s)}{s + a})? I'm sure if it can be evaluate. Homework Equations The Attempt at a Solution

I can't seem to part of an inverse Laplace transform correct. \begin{align*} f(t) &= \frac{6}{5}\mathcal{L}^{-1}\bigg\{\frac{1}{s + 2}\bigg\} + \frac{3}{5}\mathcal{L}^{-1}\bigg\{\frac{3s - 1}...

How do you find the inverse of metric tensor when there are off-diagonals? More specifivally, given the (Kerr) metric, $$ d \tau^2 = g_{tt} dt^2 + 2g_{t \phi} dt d\phi +g_{rr} dr^2 + g_{\theta \theta} d \theta^2 + g_{\phi \phi} d \phi^2 + $$ we have the metric tensor; $$ g_{\mu \nu} =...

Here is the question: I have posted a link there to this thread so the OP can view my work.

In the Math Challenge Forum it has been requested fo compute the series... $\displaystyle S = \sum_{n=1}^{\infty} \tan^{-1}\ \frac{\sqrt{3}}{n^{2} + n + 3}\ (1)$ ... and that has been performed using the general identity... $\displaystyle \sum_{n=1}^{\infty} \tan^{-1}\ \frac{c}{n^{2} + n +...

Just curious: Are there any unique relationships b/w the inverse of a function and the original, specifically when considering the derivative and integral?

If f and g are inverse functions and f ' is continuous, prove that: [from a to b] ∫ f(x) dx = b f(b) - a (a) - [from f(a) to f(b)] ∫ g(y) dy Hint: Use part (a) and make the substitution y = f(x) I have been trying to rearrange the equations and have looked online at answers, and still...

If g(a) \neq 0 and both f and g are continuous at a, then we know the quotient function f/g is continuous at a. Now, suppose we have a linear operator A(t) on a Hilbert space such that the function \phi(t) = \| A(t) \|, \phi: \mathbb R \to [0,\infty), is continuous at a. Do we then know that...

Hi, All: Let ## f: X → Y ## be a differentiable map , so that ## Df(x)≠0 ## for all ##x## in ##X##. Then the inverse function theorem guarantees that every point has a neighborhood where ##f ## restricts to a homeomorphism. Does anyone know the conditions under which conditions a map like...

Can someone explain why the answer is D a < 0 because it finishes downwards e < O because the y-intercept is in the negatives. b, & d = zero (but i don't get this) c is supposedly > 0 (nor do i get this) According to the solutions the graph is an even function, and symmetrical about the...

Hello, Homework Statement I would like to find the inverse Z transform of the following: F(z)=1-1.25z-1+0.25z-2/[1-(5/6)z-1+(1/6)z-2] using (a) partial fractions, and (b) residue theorem I have obtained different results and hence would appreciate some insight on the discrepancy and how...

I know potential has an inverse relationship with distance. However what is the equation that deduces this?

Homework Statement Find ##(g_ig_j)^{-1}## for any two elements of group ##G##. Homework Equations For matrices ##(AB)^{-1}=B^{-1}A^{-1}## The Attempt at a Solution I'm not sure how to show this? I could show that for matrices ##(AB)^{-1}=B^{-1}A^{-1}##. And that for numbers...

We have a matrix with dimension NxN.For some m belongs to N,m0 we have A^m0=0.We consider the exponential matrix e^A=I+A+A^2/(2!)+A^2/(3!)+A^m/(m!).Find the inverse matrix of e^A. I tried to write the e^A=e^A(m0)+A^m/(m!) or (e^A)^(-1)=(...

I'm looking for solutions to this problem: Matrices A(m,n) and B(n,m) satisfy AB=I(m,m) where n isn't equal to m. Can I find a matrix S(m,n) such that SA=I(n,n) or SA approximates I(n,n)? By approximate I don't have preferred definition, hence any suggestion is welcome!

Homework Statement ##\mathcal{L}^{-1}\Big\{\frac{s}{(s^2+1)^2}\Big\}## I'm trying to figure out how to find the inverse Laplace transform of this expression. Is this something you just look up in a table or is there a way to find it directly, maybe by Convolution?

Hi, a long time ago, back in high school, I remember my teacher was explaining the force of gravity to us. He gave us the equation for the force of gravity, which was proportional to the inverse square of the distance. However, he later said that something about Einstein and other researchers...

Homework Statement A patrol car is 50 ft from a long warehouse. The revolving light on top of the car turns at a rate of 30 rotations per minute. How fast is the beam of light moving along the warehouse wall when the beam makes a 45° angle with the line perpendicular from the light to the...

Is it just ∇-1 with the vector hat?

Homework Statement Given the function f(x) = (abs(x))*x +6, find f^-1(x) Homework Equations The Attempt at a Solution for x≥ 0, f(x) = x^2 + 6 y=x^2 +6 x = √(y-6) for y≥6 → f^-1(x) = √(x-6) for x≥6 for x< 0, f(x) = -x^2 + 6 y= -x^2 +6 x = √(6-y) for y<6 → f^-1(x) = √(6-x) for x<6 But...

For the given function i have to find if is surjective/injective and find the inverse of the function: $$f(x)=\frac{3x-2}{x+2}$$ I now that for inverse i have to express $x$ somehow,but i don't know how to do it... Thank you for the help!

Inverse trig problem -- please help! Homework Statement tanx+tan2x+root3tanxtan2x=root3 find x... Homework Equations The Attempt at a Solution i have tried a lot and always ended with a complicated cubic equation... please help me by giving me a another approach to the solution

Here is the question: I have posted a link there to this thread so the OP can see my work.

Hello, I have another question regarding inverse matrices. I need to find \[a^{2}\] given: \[\exists x: \begin{pmatrix} 1 &a \\ 2a &1 \end{pmatrix}^{2}\cdot \begin{pmatrix} 1\\ x \end{pmatrix}=\begin{pmatrix} 0\\ 0 \end{pmatrix}\] Any hints or guidance will be appreciated ! Thanks !

Hello all, I have this matrix A \[A=\begin{pmatrix} 1 &2 &3 &4 \\ 9 &8 &2 &0 \\ 17 &2 &0 &0 \\ 1 &0 &0 &0 \end{pmatrix}\] B is defined as the inverse of A. I need to find the element in the first row and fourth column of B, without using determinants, so without using adjoint. How should I...

prove the function ## g: \mathbb{N} \rightarrow \mathbb{N} ## ## g(x) = \left[\dfrac{3x+1}{3} \right] ## where ## [y] ## is the maximum integer part of r belonging to integers s.t. r less than or equal to y is surjective and find it's inverse I know this function is bijective, but how do I...

Hello MHB, I am aware of there is two way, u can use chain rule or defination of derivate. I totaly understand the proof with this type Derivative of Inverse Function but is that a valid proof? How ever our teacher did proof this with derivate defination which I don't understand from my...

I confront an integration with the following form: \int d^2{\vec q} \exp(-a \vec{q}^{2}) \frac{\vec{k}^{2}-\vec{k}\cdot \vec{q}}{((\vec q-\vec k)^{2})(\vec{q}^{2}+b)} where a and b are some constants, \vec{q} = (q_1, q_2) and \vec{k} = (k_1, k_2) are two-components vectors. In the...

Find the Inverse Laplace of 1/(s^3) is there some special rule for cube? The answer is t^2/2 Looking at the Laplace Table t^n looks similar but its not it exactly. What should I do?

Assume that $$ f: E \to Y \,\,\, , E \subset X$$ then can we say that $$f(E^c)=f(E)^c$$ what about the inverse mapping $$f^{-1}: V \to X \,\,\, , V\subset Y$$ do we have to have some restrictions on f and its inverse ? My immediate answer is that we have to have a bijection in order to conclude...

Homework Statement If f(x) = the third root of (x-8), find the derivative of its inverse. Homework Equations The derivative of its inverse = 1/f'(f^-1(x)) or 1 over its derivative at its inverse. The Attempt at a Solution I followed both the formula to verify my solution and...

Homework Statement I wish to prove that for s>1 $$ \sum\limits_{n=1}^{\infty}\frac{\mu(n)}{n^s}=\prod_{p}(1-p^{-s})=\frac{1}{\zeta(s)}. $$ The Attempt at a Solution (1) I first showed that $$ \prod_{p}(1-p^{-s})=\frac{1}{\zeta(s)}. $$ It was a given theorem in the text that $$...

[SOLVED] Inverse signs on both sides of an equation [Confusion] Hey everyone, I've just reinserted myself in maths after so many years, done a lot of review but I sometimes fall on small "glitches" between my test answers and the suggested answers in my textbook. I've been getting confused...

Let F_{K}: \hat{K} \to K be defined as follows: F_{K}(\hat{x},\hat{y}) = B_{K}\left[\begin{array}{c} \hat{x}\\ \hat{y}\\ \end{array}\right] + b_{K} i.e. F_{K} maps from (\hat{x},\hat{y}) to (x,y). In a more concrete sense, for this example take the following: B_{K} =...

Homework Statement Area enclosed by y=g(x), x=-3, x=5 and x-axis where g(x) is inverse function of ##f(x)=x^3+3x+1## is A, then find [A] where [.] denotes the greatest integer function. Homework Equations The Attempt at a Solution Honestly, I see no way to proceed here. Finding...

Homework Statement Y=abs -4(x+3) +1 Note: the 1 is outside the absolute value Homework Equations Switch y and x The Attempt at a Solution So you subtract the 1 to bring it to the other side After that do I put: x-1= -4(y+3) And x-1= 4(y+3) And solve for y? Am I doing...

Hi, Can anyone help me to inverse the below matrix by row reduction method. I know determinant method but I don't know row reduction method please help me. 4 5 -2 6 thanks.

Homework Statement Find X. Given the following Equation2.094 radians =tan^-1(2*x*(1.11)/1-(1.11)^2) Homework Equations The Attempt at a Solution How do you get rid of inverse tangent? Here's what i got tan(2.094((180/pi))*(1-(1.11)^2) / 2*1.11 = X

This came up when I was trying to evaluate to a decimal value an arcsec(something), but on TI-83 there is no inverse secant button. So, I punched 1/(arccos(something)). Naturally, this came up as a domain error. Then my instructor pointed out arcsesc is not 1/arccosx. Oops. Thinking about...

Please refer to the attachment. For part a) so far I have: $e^x = 1 + \frac{x}{1!} + ...+ \frac{x^n}{n!}$ So $S^\frac{-1}{2}e^\frac{-1}{S} = S^\frac{-1}{2}(1 -\frac{1}{S} + \frac{1}{2!S^2} - \frac{1}{3!S^3} + \frac{1}{4!S^4} + ... - ...)$ I don't think my $S^\frac{-1}{2}$ on the outside is...

Homework Statement Find (f−1)'(a). f(x) = 5x^3 + 3x^2 + 5^x + 4, a = 4 Homework Equations I'm not entirely sure but I assume I have to use d/dx(f-1) = 1/f '(f-1(x)) The Attempt at a Solution So far I switched y and x. Found dx/dy to be 15y^2 + 6y + 5. Then I switched dx/dy to...

Homework Statement Hey guys, So I have the following permutations, which are a subgroup of S3: σ_{1}=(1)(2)(3), σ_{5}=(1,2,3), σ_{6}=(1,3,2) This is isomorphic to Z3, which can be written as {1,ω,ω^{2}} Next, we have the basis for the subgroup of S3: e_{i}=e_{1},e_{2},e_{3} And we also have...

Homework Statement Evaluate sin^-1(cos70°) Homework Equations The Attempt at a Solution sin^-1(cos70°)=θ sinθ=cos70° sinθ=1/2 sinθ=∏/3

Homework Statement f(x)= 2x + x^2 Homework Equations The Attempt at a Solution I don't know how to make x the subject

Hey guys! Basically, I was wondering how to prove the following statement. I've seen it in the Hamermesh textbook without proof, so I wanted to know how you go about doing it. Let's say you have a group element g_{1}, which has a corresponding inverse g_{1}^{-1}. Let's also define a linear...

Homework Statement ##{\Lambda_c}^b## is a Lorentz transformation and ##{\Lambda^c}_b## is its inverse, so ##{\Lambda_c}^b {\Lambda^c}_b## gives an identity matrix. How can I write this, assuming it's possible, in terms of ##\delta##'s ? Homework Equations The Attempt at a...

can a function that's not inversable be inversible in certain interwalls. is it ok to say its inversable in this specific intervall or can't the function ever be called inversible?

again, i need some help here guys.$\displaystyle\int\frac{3x-1}{2x^2+2x+3}dx$ =$\displaystyle\int\frac{3x-1}{2\left[\left(x+\frac{1}{2}\right)^2+\frac{5}{4}\right]}dx$ $\displaystyle a=\frac{\sqrt{5}}{2}$; $\displaystyle u=x+\frac{1}{2}$; $\displaystyle du=dx$; $\displaystyle x=u-\frac{1}{2}$...

Homework Statement $${ { L } }^{ -1 }\{ \frac { s }{ { ({ s }^{ 2 }+1) }^{ 2 } } \} +{ { L } }^{ -1 }\{ \frac { 1 }{ { ({ s }^{ 2 }+1) }^{ 2 } } \}$$ Homework Equations The Attempt at a Solution I used ##{ { L } }\{ { t }^{ n }f(t)\} ={ (-1) }^{ n }\frac { { d }^{ n } }{ d{ s...