Inverse Definition and 1000 Threads

Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?

Homework Statement I need to find the inverse of y=x+√(x^2-1) Homework Equations The Attempt at a Solution I know it's undefined from x=-1 and x=1 so there must be two different inverse functions on two different intervals. I don't know how to find them though.

Homework Statement You know the U substitution proofs for inverse trig functions that go like this: \int\frac{1}{a^{2}+x^{2}}dx \int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx let u = x/a du= dx/a ... \frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...

How to write the algorithm? I figured out a method to find the inverse. The assignment is making use of the property of triangular matrices to find the inverse of a matrix \displaystyle A. The inverse of a triangular matrix(Upper/ Lower) is also triangular(Upper/ Lower) and is easy to find...

Homework Statement The function f(x) has an inverse function, g(x). Find g'(5). Homework Equations f(x) = x^5 + 2x^2 + 2xThe Attempt at a Solution I don't see how I can possibly find the inverse of this function. So I opted to use the derivative rule for inverses. f'(x) = 5x^4 + 4x + 2 5...

Hi, I am taking a random process class and I came across a problem that has stumped me. I believe I know the end result but I would like to know how it is solved. I have been out of college for a while and I am a little rusty with integration. Homework Statement What I need is to find out...

Hello everyone. I am slightly confused by these ideas so i would like your help. How is additive inverse defined? Is unary negation an operation in its own right just like those more familiar, like addition, multiplication? Or something else?

In the recommended format :) Homework Statement First we say that f:S→T is a map. If Y ⊆ T and we define f-1(Y) to be the largest subset of S which f maps to Y: f-1(Y) = {x:x ∈ S and f(x) ∈ Y} I must prove that f[f-1(Y)] = Y for every subset Y of T if, and only if, T = f(S). Homework...

Hi guys, my first post here. This isn't homework or anything, just a personal project. Homework Statement I need to find the inverse of the relative mercator equation. That is, given an origin latitude/longitude, find the current latitude/longitude from an x,y point. Because longitude is...

Homework Statement Consider the central force F=-k/(r^3) u(hat in r direction). This is an attractive force. For various values of k, explain what the orbit of a particle about a force center looks like. Homework Equations Included within question. The Attempt at a Solution I am not quite...

Homework Statement Let g(x) = (e^x - e^-x)/2. Find g^-1(x) and show (by manual computation) that g(g^-1(x)) = x. Homework Equations g(x) = (e^x - e^-x)/2 The Attempt at a Solution I get the inverse = ln[ (2x + sqrt(4x^2 + 4) ) / 2 ] How do I proceed?

What is the fastest way to find the inverse of a 4x4 matrix? The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.

Homework Statement I'm having problems with finding the inverse equation for this function e^x/(e^x-1) The Attempt at a Solution Currently, I have done about 2 methods to solve it and hitting dead-ends on each one: Attempt 1. x=e^y/(e^y-1) then multiply both sides by (e^y-1) so...

Homework Statement Find the derivative of: 1. f(x)=arccos(5x^3) 2. f(x)=∫cos(5x)sin(5t)dt when the integral is from 0 to x Homework Equations Chain rule, dy/dx=dy/du*du/dx The Attempt at a Solution For the first one, I can just take 5x^3 as u and then apply the chain rule...

maple issue -- inverse laplace transform equation from a basic series RLC circuit Pretty simple for some of you I know, but I have a laplace transform equation from a basic series RLC circuit ((sV-v(0))/L+si(0))/(s^2+sR/L+1/LC) = I(s) I want to take the inverse laplace of it, I am given all...

Homework Statement Homework Equations The Attempt at a Solution for 24. which is a quadratic function, i understand that you have to exchange the positions of x and y and solve from there...but my question is the inverse function of that quadratic for 24 is a negative number...

Homework Statement : Define f: ℝ→ℝ by f(x)=x^2. Find f^-1(T) for each of the following: (a) T = {9} (b) T = [4,9) (c) T = [-4,9] The attempt at a solution: So, the inverse of f should be f^-1(T)=+/-√(x). Therefor: (a) f^-1(9)= +/- 3 (b) f^-1(4)= +/- 2, f^-1(5)= +/- √(5), f^-1(6)= +/- √(6)...

Homework Statement The graph of y=f(x) is shown below. http://Newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data Rank the following from smallest(1) to largest(4). f−1(0) f(0) f(5) f−1(5) Homework Equations none available The...

Here is my problem: cot(arcsin(x)) my awnser: cot= x/(1-x)^1/2 The online program were suppose to use says I am wrong but I am not sure what I did wrong.

Evaluate the integral \int \frac{x}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, dx by making the substitution u = x^{2}Homework EquationsThe Attempt at a Solutionu = x^{2} - 4 so \frac{du}{2}= xdx \int \frac{1}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, xdx \frac{1}{2} \int \frac{1}{(u) \sqrt{x^4 - 8x^2}} \...

Homework Statement The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and...

Hello PF! I've got a strange question for you physics boffins; assuming for a moment that lasers obeyed the inverse square law, what range would a typical 1mW red laser have in the atmosphere?

Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...

Homework Statement Given y = 2/3(arctan \frac{x}{4}), find x. Homework Equations Inverse trigonometric identities for tan. (I guess)The Attempt at a Solution I never attempted because it seems impossible for me. You think this is possible? Thank you!

EDIT: 1.Homework Statement The problem asks to simplify this: cos(arcsin x)Homework Equations let arc sin x = θThe Attempt at a Solution EDIT: I have to edit because I received a warning for not posting for #3 and #2. I originally posted "cos(arcsin x)" for #2 because that was what I know...

Homework Statement Find the inverse of a rational function: f(x)=\frac{2x}{x-2} The Attempt at a Solution 1. Verify the function is one-to-one. Question: is there a way to do that withought drawing the graph? Some algebraic method? I know that this means that the function crosess any given...

Consider the function f: R-->R where F(x)= x, if x<1 x², if 1<x<9 (read x <or equal to 1 and x< or equal to 9) 27*sqrt(x), if x>9 I know that f is not differentiable at x=1 and x=9 because the derivative at each one of these points don't exist once the lateral limits don't coincide.(Is...

Homework Statement How do I find out the exact value of tan^-1 (1 / sqrt(3))? Homework Equations nada The Attempt at a Solution I don't know where to start.

Hi all, I've been trying to solve the following I = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{x}{(x^2+y^2+d^2)^{\frac{5}{2}}} e^{-i(kx+\ell y)} \ dx \ dy where d,k,\ell are constants. I haven't been able to put this into a tractable analytic form and I figured I'd consult all...

Hello how can we know with the definition of inverse function this function is inverse function or not? ? another questions. this function is inverse function because but if we have this function we can't do the same approach.why?(and it isn't a inverse function)...

I was asked this question on a test I just took and I was kinda stumped. I worked it out but I think I did it incorrectly so I was hoping for some input. Thanks. 'A' is a 3x3 matrix and 'I' is the identity matrix for a 3x3. Find the Inverse of 'A' given...

Homework Statement I'm trying to solve the derivative of this equation: 1-(x*arcsin(x))/√(1-x^2 ) I've straight away disregarded the 1 as it will be 0 so I'm left with -(x*arcsin(x))/√(1-x^2 ). The Attempt at a Solution I've applied the quotient rule and labelled U= -x*arcsin(x) and...

I understood that for a direct proportion such as "if 6 mangoes cost $12, then how many dollars worth are 12 mangoes?", we have to first divide 12 by 6 to get the no. of divisions of 6 in 12 i.e. precisely 2 and then as 1 division is worth $12 we multiply the two divisions with $12 and that's...

Hi. I am reviewing for an exam, and this is a topic that I did not go through very thoroughly. I understand how to calculate the derivative of an inverse function when I am given a point, as I simply use the equation (1/f((f^-1))'. So if I am given the equation y=x^3, for example, and am asked...

Hello All: Suppose I have a completely known linear system: A*x=b. I know the matrix A, and an x and the associated RHS vector b (and it is non-trivial). Is there some tricky way to directly determine the inverse of A without performing an inversion by typical means (Gauss elimination, LU...

Homework Statement Let A be an m x n matrix, and suppose there exist n x m matrices C and D such that CA = In and AD = Im. Prove that C = D. Homework Equations The Attempt at a Solution I think it's obvious that C=D=A^(-1). But I'm having trouble proving it since I cannot prove...

Hi guys :) I'm looking to get a jump start on my uni course and have been going through some topics on my own before classes start in the Fall, I've reached the point of Laplace Transform and Fourier maths - and it's tough! I have a small question on an inverse laplace transform equation in...

Homework Statement find dz/dy(partial) z= tan-1(y/x) Homework Equations The Attempt at a Solution z= tan-1(y/x)let u=y/x z= tan-1(u) dz/du = 1/ (1+u2) so dz/dy = dz/du (du/dy) du/dy = 1/x so dz/dy = (1/1+u2)(1/x) = 1/ 1+ (y2/x2) * 1/x = 1/ x + (y2/x2)x) = x / x + y2but I should be...

Homework Statement f(x)=3+x2+tan((πx)/2) where -1<x<1...then find f^-1(3) Homework Equations y=3+x2+tan((πx)/2) The Attempt at a Solution i jave ried to solve first for x and then interchange the x and y,bu i am having problem with the trignometric identity used here...

Hi everybody I have a question that I have a guess for the answer but I want to be sure I have an identity C=A*B where A,B,C are matrices and in general they are not square is there a way to find A in terms of B and C by using pseudo inverse matrix or using pseudo inverse might help me in...

Homework Statement We did an experiment using resistance putty and a multimeter. We changed the radius of the putty but kept the length the same. We recorded the resistances at different radius'. I know that physics theory says that resistance is inversely proportional to cross-sectional...

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

Hello, this is related to my research on RCW(FMM) analysis of light shone onto crossed gratings. main question: can you exploit having matrix A and its inverse A^{-1} to calculate the eigen vectors/values of A in a more effective way? backgroud: so my problem is this: I have an unusual...

I am aware that, in statistics, things get difficult as soon as they get nonlinear. And taking the reciprocal of a quantity is a nonlinear operation. I have some data that would form a nice looking straight line, except for random error scattering it around the line. I have a total of about...

y = 3^-x + 9^-x ln(y) = ln(3^-x + 9^-x) don't know where to go from here.

Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given. You have : y = x^2 - 4 x = y^2 - 4 y^2 = x + 4 y = ± sqrt(x+4) I don't get why there is a ± symbol there. My book says that it's necessary because there are two...

Hi, I am trying to solve the integral of the Inverse Gamma Distribution. Does this equate to 1 as it is a pdf? Thanks

i read this sentence like a 100 times and i still don't get it please can anyone help me?? PEAK INVERSE VOLTAGE (PIV): PIV is the maximum reverse bias voltage which can be applied safely to a diode without its breaking down. Beyond this voltage a diode breaks down they say the PIV must be...

Homework Statement Problem reads: find inverse Laplace transform of f(t) of F(s)=(2s+3)/(s(s2+7s+10) What is the value of the function f(t) at t=0 and t=∞?Homework Equations Inverse laplace transformThe Attempt at a Solution I solved F(t) down to F(t)= .3/s+0.166/s+2-0.465/s+5 thus lead me to...

I have written some routines that compute the 2D inverse Fourier transform, if anyone thinks that this may be useful at all then please let me know and I will gladly post the code.