Inverse Definition and 1000 Threads

  1. Italo Campoli

    Inverse Laplace (stuck @ Partial Fraction)

    Homework Statement Find the Inverse laplace transform of: http://www4c.wolframalpha.com/Calculate/MSP/MSP14541hg721e74730d4fb00004644i96f59549h1d?MSPStoreType=image/gif&s=30&w=201.&h=40. Result...
  2. M

    What is the Inverse Cosine of a Squared Angle?

    Not sure if I'm doing this right. I have an angle theta to find but the cosine has been squared. I brought over inverse cosine to multiply to leave theta on its own. I was told the answer should be closer to 37 degrees? Am I doing something wrong here?
  3. S

    Full Rank Matrix: Determinant Condition | Rank-Nullity Theorem

    Homework Statement Show that the matrix ##A## is of full rank if and only if ##ad-bc \neq 0## where $$A = \begin{bmatrix} a & b \\ b & c \end{bmatrix}$$ Homework EquationsThe Attempt at a Solution Suppose that the matrix ##A## is of full rank. That is, rank ##2##. Then by the rank-nullity...
  4. Unichoran

    Calculating Inverse Functions for Hourly Salary and Production Units

    Homework Statement Hello,I have some problems with my Pre-Calculus homework. The task is: You get paid 8$ per hour plus 0.85$ per unit you produced. 1.Set up an equation for it. 2.Find the inverse function. 3.What does each variable in the inverse function mean? Homework Equations See below...
  5. Italo Campoli

    Inverse Laplace Transform of a fractional F(s)

    Homework Statement [/B] Having a little trouble solving this fractional inverse Laplace were the den. is a irreducible repeated factor 2. The attempt at a solution tryed at first with partial fractions but that didnt got me anywhere, i know i could use tables at the 2nd fraction i got as...
  6. M

    Integration: inverse trigonometric functions

    Homework Statement ∫(t/√(1-t4))dt Homework Equations ∫(du/√(a2 - u2)) = arcsin (u/a) + C ∫(du/(a2 + u2) = (1/a) arctan (u/a) ∫(du/(u√(u2 - a2))) = (1/a) arcsec (|u|/a) The Attempt at a Solution Edit: I meant to write u where t2 is[/B]
  7. J

    Checking for Accuracy in homework

    I noticed the scan was cut off on the second image at the bottom right, but I came up with x= 31/5 My first test in Calc I begins tomorrow and I want to know that I'm headed in the right direction. I think I understand to some extent how logarithms can be expanded and condensed though I'm...
  8. D

    Lorentz transformation matrix and its inverse

    Given the Lorentz matrix Λuv its transpose is Λvu but what is its transpose ? I have seen ΛuaΛub = δb a which implies an inverse. This seems to be some sort of swapping rows and columns but to get the inverse you also need to replace v with -v ? Also In the LT matrix is it the 1st slot...
  9. DeldotB

    Show a functions inverse is injective iff f is surjective

    Hello all, Can anyone give me a pointer on how to start this proof?: f:E\rightarrow F we consider f^{-1} as a function from P(F) to P(E). Show f^(-1) is injective iff f is surjective.
  10. E

    Blackbody Radiation and the Inverse Square Law

    I am currently confused with the concept of the blackbody radiation and the inverse square law. Planck's function for the radiation of a blackbody is in ##W sr^{-1} m^{-3} ##, is this somehow a form of intensity (because of the watts per square meter unit)? If it does, doesn't intensity...
  11. Ebenshap

    How inverse square law is derived from area of sphere

    I almost understand how the inverse square law is derived from the area of sphere equation, 4πr2, but I'm not quite clear on what happens to the 4π. I found one equation that seemed to say that the intensity is equal to the area of the sphere of the source point times the amount of whatever...
  12. kandelabr

    A Least-squares - fitting an inverse function

    I have a set of data points that I must fit to an inverse function like this: y(x) = a/(x+b) + c My problem is that least-squares fitting using this equation is extremely unstable and heavily dependent on initial guess. No matter how accurate parameters I start with, the algorithm often goes...
  13. P

    Proving Inverse Functions: Multiplicative Relationships

    Is there a way to formally prove that if ##f## and ##g## are multiplicative inverses of each other, then ##f^{-1} (x) = g^{-1} (\frac{1}{x})##?
  14. J

    Inverse function of a quarter circle gives me same function

    Is this normal? it doesn't seem correct. The equation for the portion of circle with radius 1 unit in the 1st Quadrant is: ## y = f(x) = \sqrt{1-x^2} ## Domain is 0<x But when I calculate f'(x) I also get ## f'(x) = \sqrt{1-x^2} ## I thought inverse functions always reflect about y=x. Please...
  15. arpon

    What is the inverse function of x + sin x ?

    What is the inverse function of ##x+sin x## ?
  16. Amrator

    Rate of Change Using Inverse Trig Functions

    Homework Statement A spectator is standing 50 ft from the freight elevator shaft of a building which is under construction. The elevator is ascending at a constant rate of 20 ft/sec. How fast is the angle of elevation of the spectator's line of sight to the elevator increasing when the elevator...
  17. ognik

    MHB Intuition for inverse hyperbolics

    Does anyone perhaps have a good way for me to get a lasting 'intuition' about what inverse hyperbolics are? I look at, for example, the well known sin x; it is periodic. Then, it seems, sinh x is a reflection of sin x about the line y=x. (I found an example at 7. The Inverse Trigonometric...
  18. anemone

    MHB Evaluate Inverse of Hi M.H.B.: Math Problem

    Hi MHB, The following problem has been a really vexing problem (for me) because I believe there would be a tricky way of approaching it but I could not solve it after working with it on and off for two days, it is an Olympiad math competition problem, and so far no one that I know of has solved...
  19. C

    The Practical Usages of Finding the Inverse of a Function

    Hi, I know that the inverse function of y= f(x) =2x+1 is y-1=2x x=(y-1)/2 and then we just replace x with f-1(y) and then when we plug in any value of y it gives us a corresponding x value. Now my question is this: If we want to find a line or function that is perpendicular to another...
  20. P

    Inverse trigonometric functions

    I am familiar with the importance of the following inverse circular/hyperbolic functions: ##\sin^{-1}##, ##\cos^{-1}##, ##\tan^{-1}##, ##\sinh^{-1}##, ##\cosh^{-1}##, ##\tanh^{-1}##. However, I don't really get the point of ##\csc^{-1}##, ##\coth^{-1}##, and so on. Given any equation of the form...
  21. P

    Inverse hyperbolic functions (logarithmic form)

    To express the ##\cosh^{-1}## function as a logarithm, we start by defining the variables ##x## and ##y## as follows: $$y = \cosh^{-1}{x}$$ $$x = \cosh{y}$$ Where ##y ∈ [0, \infty)## and ##x ∈ [1, \infty)##. Using the definition of the hyperbolic cosine function, rearranging, and multiplying...
  22. E

    Solving inverse binomial equation

    Hello all, I have this equation \sum_{k=\lceil \frac{n}{2}\rceil}^n{n\choose k}P^k\left(1-P\right)^{n-k}=\epsilon and I want to find P as a function of epsilon and n. Can I do that? If so, then how? Note: \epsilon<10^{-3} if it helps for any possible approximation. Thanks
  23. J

    Simple inverse Laplace using PFE not so simple?

    Hello, When evaluating the step response of a circuit, the resulting Laplace representation is: $\frac{I_{pd}}{s^2 C1 R1}$ If I look this up on a table of Laplace Transforms, this results in $\frac{I_{pd}*t}{C1 R1}$. However, I'm struggling to solve this via partial fraction expansion--is...
  24. G

    Inverse of diagonal dominant matrices

    Homework Statement Show that ##n\times n ## complex matrices such that ##\forall 1\le i \le n,\quad \sum_{k\neq i} |a_{ik}| < |a_{ii}|##, are invertible Homework EquationsThe Attempt at a Solution If I show that the column vectors are linearly independent, then the matrix has rank ##n## and...
  25. J

    Torus parametrization and inverse

    I've been looking at the torus parametrization \begin{equation} \phi(u,v)=((r\cos u+a)\cos v, (r\cos u +a)\sin v, r\sin u) \end{equation} with \begin{equation}a>0, r\in(0,a)\end{equation}. I want to invert this map to get a chart map for the torus. Can anyone give me a hand with this? Thanks!
  26. S

    Inverse Discrete Laplace Transform

    Hi, I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar. The first two are the laplace transform. The third line is the Fourier Transform. The...
  27. P

    MHB Johnsy's question over Facebook about an Inverse Laplace Transform

    To start with, apply partial fractions... $\displaystyle \begin{align*} \frac{A\,s + B}{ s^2 + 9} + \frac{C\,s + D}{ \left( s^2 + 9 \right) ^2 } &\equiv \frac{ 4s^3 + 5s^2 + 57s + 45}{ \left( s^2 + 9 \right) ^2 } \\ \left( A\,s + B \right) \left( s^2 + 9 \right) + C\,s + D &\equiv 4s^3 + 5s^2 +...
  28. B

    Proving Left Inverse of Injective Function

    Homework Statement ##f : A \rightarrow B## if and only if ##\exists g : B \rightarrow A## with the property ##(g \circ f)(a) = a##, for all ##a \in A## (In other words, ##g## is the left inverse of ##f##) Homework EquationsThe Attempt at a Solution I have already prove the one direction. Now I...
  29. K

    Why does an inverse exist only for surjective functions?

    In other words, why does a function have to be onto (or surjective, i.e. Range=Codomain) for its inverse to exist?
  30. Euler2718

    What is the Correct Integral of Inverse Cosecant?

    Running into a little trouble when doing this integral by hand: \int arccsc(x) dx u = arccsc(x) \implies du = -\frac{1}{x\sqrt{x^{2}-1}} dx dv = dx \implies v = x \int u dv = uv - \int vdu \int arccsc(x) dx = xarccsc(x) - \int x\cdot -\frac{1}{x\sqrt{x^{2}-1}} dx \int...
  31. E

    Inverse Z transform - contour integration

    Hi! Here is my task: Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$, if $$|z|>\frac{2}{3}$$ using definition formula. I found that $$x(n)$$ is $$\frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using other method). But how can I find it using definition formula, $$x(n)=\frac{1}{2\pi j}\oint_{C}^{ }...
  32. END

    Inverse Laplace Transformation

    Homework Statement Solve the following: $$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$ Homework Equations Table of Laplace Transforms.The Attempt at a Solution The solution is $$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$ I know I need to break up ##F(s)## into...
  33. E

    Inverse Z Transform of X(z): Finding x(n) for Causal Signal

    Hi! My task is to find discrete signal x(n), if z transform of that signal is $$X(z)=\frac{5}{(z-2)^{2}}$$. It is known that signal is causal. Here is what I have done. Since signal x(n) is causal, convergence of z transform of that signal will be outside of circle with radius r: We have in...
  34. jk22

    Quantum Measurement Operator and Results: Exploring the Inverse Bell Theorem

    if we consider a separable measurement operator $$(A+A')\otimes (B-B')$$ then quantum mechanics predict the result is in [-2;2] Whereas going to classical results would give in [-4;4] This could indicate that going from measurement operator in the quantum realm to measurement results is maybe...
  35. R

    Finding the sum of inverse trigonometric expression

    Homework Statement Find ## \sum_1^{23} tan^{-1}(\frac{1}{n^2+n+1}) ## Homework Equations ## tan^{-1}x + tan^{-1}y = tan^{-1}(\frac{x+y}{1-xy} )##The Attempt at a Solution I think we have to split the question in a form of relevant equation given above. First thing what should I do?
  36. A

    H(z) = (z2 + 0.5z - 0.5)/(z2 + 1.5z + 0.5)

    Homework Statement Homework Equations H(z) = Y(z)/X(z) The Attempt at a Solution I realized this wasn't in partial fraction form because the 1+z-1+0.5z-2 has non-real roots. I multiplied the 1st fraction part by z1 and the 2nd fraction by z2, then I combined them into one fraction and I...
  37. B

    Relationship between inverse matrix and inertia tensor?

    Seems exist some relationship between the inverse of a matrix with the inertia tensor, looks: This relationship really exist?
  38. B

    Computing the Inverse of a Cubic Matrix

    Be the matrix A defined by [aijk] (a matrix 2x2x2), do you know how to compute a inverse this cubic matrix?
  39. R

    Inverse Laplace Transform with e^{a s}

    Homework Statement How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$? I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...
  40. B

    Is f(x) = √(5x+2) one-to-one on (-2/5, infinity)?

    Homework Statement Show that f(x) = \sqrt{5x+2} is one-to-one. Homework Equations If f' >0 or f' < 0 everywhere on f's domain, f is one-to-one. The Attempt at a Solution f^\prime = \frac{5}{2} \frac{1}{\sqrt{5x +2}} = \frac{5}{2f} f' is positive on (-2/5, infinity) but is undefined...
  41. S

    MHB Determining one to one and finding formula for inverse help needed

    I have a problem I am trying to solve but no example provided can clarify the steps. I find this to be the problem with math examples, they provide problems but utilize same numbers so people who are not as math savvy such as I cannot figure the steps out as easily as they are provided. Anyway...
  42. Galbi

    How can I calculate the inverse of a 4th order tensor?

    Homework Statement I'm looking for how to calculate inverse of the 4th order tensor. That is, A:A-1=A-1:A=I(4) If I know a fourth order tensor A, then how can I calculate A-1 ? Let's just say it is inversible. Homework EquationsThe Attempt at a Solution
  43. E

    MHB Inverse Theorem and Fermat's Theorem (Iso point)

    Hello, I've been using Caratheodory's Lemma to prove the Inverse Function Theorem and Fermat's Theorem. I have managed to prove both of them, I would just like someone to look over my proof and tell me if I'm missing anything (i.e. should I clarify any parts of my proof). So here goes: Inverse...
  44. Cookiey

    Inverse Function of Greatest Integer Function in a Given Domain

    Homework Statement If f:(2,4)-->(1,3) where f(x)=x-[x/2] (where[.] denotes the greatest integer function), then find the inverse function of f(x). Homework Equations (None I believe.) The Attempt at a Solution I know that for a function to be invertible, it must be both one-one and onto...
  45. K

    How Does Constant Electric Field Affect Piezoelectric Crystal Dimensions?

    Homework Statement Piezoelectric crystals will change about 0.1% of their static dimension when an external electric field is applied to the material. Homework Equations 1. What happens with the static dimension if the external electric field applied is a constant? 2. Will the static dimension...
  46. K

    How Does the Inverse Piezoelectric Effect Alter Crystal Dimensions?

    Hi, I'd like to get some help with my homework. Piezoelectric crystals will change about 0.1% of their static dimension when an external electric field is applied to the material. 1. What happens with the static dimension if the external electric field applied is a constant? 2. Will the static...
  47. Math Amateur

    MHB Inverse image of a set under the restriction of a function

    I am reading Munkres book, "Topology" (Second Edition). I need help with an aspect of Theorem 18.2 Part (f) concerning the inverse image of a set under the restriction of a function ... Theorem 18.2 Part f reads as follows: In the above text we read: " ... ... Let V be an open set in Y...
  48. Math Amateur

    MHB Finding inverse of F in Munkres' Topology Ch.2 EX 5 pg 106

    In Munkres book "Topology" (Second Edition), Munkres proves that a function F is a homeomorphism ... I need help in determining how to find the inverse of F ... so that I feel I have a full understanding of all aspects of the example ... Example 5 reads as follows:Wishing to understand all...
  49. T

    Derivative of an inverse function

    Homework Statement I will post a picture of the problem and then the second picture will be my work. The problems are the first two. Homework EquationsThe Attempt at a Solution I didn't know how to do this at first so I don't know if I am doing it correctly now. Also I don't know the correct...
  50. G

    Prove arccos(-x)+arccos(x) = pi

    Homework Statement From an old edition of the Anton calculus text, I am asked to prove cos-1(-x) + cos-1(x) = π or equivalently cos-1(-x) = π - cos-1(x) Homework EquationsThe Attempt at a Solution Earlier I proved that sin-1(x) was odd by noting sin-1(sin(x)) = -sin-1(sin(-x)), so I...
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