Functions Definition and 1000 Threads

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.

Homework Statement question: State two different functions that have same range but different domain. Then tell me what is the range of those two functions. The attempt at a solution Y = x/2 Y= x/2 +1 I don't know if that is correct or not. Any suggestion will help.

Suppose we define the measurement of an observable A by v(A) v being an 'algorithm giving out one of the eigenvalues each time it is called' (we accept the axiom of choice) In this context we have in particular v(A)≠v(A) since when we call the left hand side and then the right handside the...

Can I present the trigonometry functions (such as SinX, CosX, TanX, CotX) by using only- Log, Lan, multiplication, division, addition, subtraction, exponantion, nth root operations?

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})##?

Homework Statement Can you create a list of which functions increase towards infinity the fastest for limit solving? Homework EquationsThe Attempt at a Solution I'm trying to make a list from least speed, to fastest speed, in approaching infinity. As in, if you have a limit, and it has...

I am confused about the order in which we apply transformations to a input of a parent function to get the corresponding input of the new function. Say for example, we have the function ##y = \sin(-2x + 1)=\sin(-2(x-\frac{1}{2}))##. Intuitively, it would seem as though we would transform a point...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.5 From Numbers to Polynomials ... I need help with an aspect of the proof of Lemma 3.70 ... The relevant text from Rotman's book is as follows:In...

Please help give references on solving the following integral: \int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx where a\neq b Thanks a lot in advance.

Came across this in a discussion of essential self-adjointedness: Let P be the densely defined operator with Dom(P) = C^{\infty}_c (\mathbb{R}) \subset L^2 ( \mathbb{R} ) and given by Pf = -i df/dx. Then P is essentially self-adjoint. It is the C^{\infty}_c (\mathbb{R}) \subset L^2 (...

#Hi All, Let ## f: \mathbb C \rightarrow \mathbb C ## be entire, i.e., analytic in the whole Complex plane. By one of Picard's theorems, ##f ## must be onto , except possibly for one value, called the lacunary value. Question: say ##0## is the lacunary value of ##f ##. Must ## f ## be of the...

This is picture taken from my textbook. I understood the last two statements "To check whether..". A function is one if its strictly increasing or decreasing. But I am not able to understand the first statement. Polynomials are continuous functions. Also, a continuous function ± discontinuous...

Homework Statement Prove that $$\sum_{r=1}^{b-1}[\frac{ra}{b}]=\frac{(a-1)(b-1)}{2}$$ where [.] denotes greatest integer function and a & b have no common factors. Homework Equations ##n\le [n]<n+1## <x> denotes fractional part of x. 3. The Attempt at a Solution I first added and subtracted...

I read somewhere that mathematical functions can be implemented as sets by making a set of ordered tuples <a,b> where a is a member of A and b is a member of B. That should create a function that goes from the domain A to the range B. But set theory has functions too, could they be sets too...

Hey. Assume you have a signal ##f## with period ##T_f## and a signal ##g## with period ##T_g##. Then the signal ##h= f+g## is periodic iff ##T_f/T_g \in \mathbb{Q}##. So if ##T_f/T_g## is an irrational number, the signal ##h## will not be periodic. Why is this actually the case?

So I've delved into programming, and gotten experienced with the fundamentals. However, the more I learn, the more I question the central object of comp. science, computation, and its foundation. According to Wikipedia, "Computation is any type of calculation that follows a well-defined model...

Hi An exercise asks to show $ \int_{a}^{b}f(z) \,dz = -\int_{b}^{a}f(z) \,dz $ I can remember this for real functions, something like $ G(x) = \int_{a}^{b}f(x) \,dx = G(b) - G(a), \therefore \int_{b}^{a}f(x) \,dx = G(a) - G(b) = -\int_{a}^{b}f(x) \,dx $ I have seen 2 approaches, either...

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...

Dear all, Could somebody please, indicate me some tutorial, in order to generate a 3D grid to plot the wave function using the Hamiltonian eigenvalues and the slater type orbitals ? Thanks in advance, Wellery

Hi I'm a bit confused about some mathematical notation If i write f(x)=(2x^2 + 10)^4 And i define u= 2x^2 +10 u^4 = f(x) Would it then be correct to write f(u)= u^4 Or would i get f(u)= 2(u)^2 +10 = (2(2x^2 +10)+10)^2 Should i define u^4 = f(x) first? Would it then be correct...

Homework Statement Determine whether or not the vector functions are linearly dependent? u=(2t-1,-t) , v= (-t+1,2t) and they are written as columns matrixes. Homework Equations Wronskian, but I don't think I should use it because I need to take derivatives so it doesn't seem like it would...

Hi - just started complex analysis for the 1st time. I have been a little confused as to the chicken and egg-ness of Cauchy-Riemann conditions... 1) Wiki says: "Then f = u + iv is complex-differentiable at that point if and only if the partial derivatives of u and v satisfy the Cauchy–Riemann...

Hi, How do you correctly use units when writing derivatives and functions in math? Example A car goes 17miles per gallon, so a function m with the equation m(g)=17g describes the distance it can go with g gallons. And the derivative dm/dg = 17 miles/gallon. Question: could you write the...

Consider two functions ##f\left(x, y\right)## and ##g\left(px, qy\right)##, where ##p## and ##q## are known. How can I plot the two functions on the same graph (i.e. the same axes)? The function ##f\left(x, y\right)## will have axes with values ##x## and ##y##, while the other will have axes...

I have been looking through the book Counterexamples: From Elementary Calculus to the Beginning of Calculus and became interested in the section on periodic functions. I thought of the following question: Suppose you have a periodic real valued function f(x) with a fundamental period T. Let c...

I am reading Joseph J.Rotman's book, A First Course in Abstract Algebra. I am currently focused on Section 3. Polynomials I need help with the a statement of Rotman's concerning the polynomial functions of a finite ring such as $$ \mathbb{I}_m = \mathbb{Z}/ m \mathbb{Z} $$ The relevant...

Sorry for the disturbance, So I have been looking (without success) for a way to define a variable within an implicit function in Java. What I really mean by this is I have the equation: In this function my program will give me all of the values except for px. I have tried rearranging the...

Suppose you have a free election and you make a measurement of its position r_0 at time t = 0. You then wait some time t required for the wave function to evolve out of its collapsed eigenstate. The electron now supposedly has a wave function expanding to infinity in all directions, albeit with...

Is there a way to motivate the sinus and cosinus functions by looking at their Taylor expansion? Or equivalently, is there a way to see that complex numbers adds their angles when multiplied without knowledge of sin and cos?

1. Given, x + yi = tan^-1 ((exp(a + bi)). Prove that tan(2x) = -cos(b) / sinh(a)Homework Equations I have derived. tan(x + yi) = i*tan(x)*tanh(y) / 1 - i*tan(x)*tanh(y) tan(2x) = 2tanx / 1 - tan^2 (x) Exp(a+bi) = exp(a) *(cos(b) + i*sin(b))[/B]3. My attempt: By...

Homework Statement This problem is not from a textbook, it is something I have been thinking about after watching some lectures on Fourier series, the Fourier transform, and the Laplace transform. Suppose you have a real valued periodic function f with fundamental period R and a real valued...

I just finished working through compositions of functions, and what properties the inner and outer functions need to have in order for the whole composition to be injective or surjective. I checked Wikipedia just to make sure I'm right in thinking that for a composition to be injective or...

Is any Irrational Roots Theorem been developed for polynomial functions in the same way as Rational Roots Theorems for polynomial functions? We can choose several possible RATIONAL roots to test when we have polynomial functions; but if there are suspected IRRATIONAL roots, can they be found...

Hi Physics Forums. I am wondering if I can be so lucky that any of you would know, if these two functions -- defined by the bellow integrals -- have a "name"/are well known. I have sporadically sought through the entire Abramowitz and Stegun without any luck. f(x,a) = \int_0^\infty\frac{t\cdot...

Let $\{p_n\}$ be a nonnegative nonincreasing sequence and converges to $p \ge 0$. Let $f : [0,\infty)\to[0,\infty)$ be a nondecreasing function. So, since f is a nondecreasing function, $f(p_n)>f(p)>0$. How did this happen?

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...

Homework Statement I've been trying to solve the following problem but can't wrap my head around it. Let ##x##, ##f(x)##, ##a##, ##b## be positive integers. Furthermore, if ##a > b##, then ##f(a) > f(b)##. Now, if ##f(f(x)) = x^2 + 2##, then what is ##f(3)##? Homework Equations The Attempt...

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...

How do I correctly compute the convolution of two delta functions? For example, if I want to compute ##\delta(\omega)\otimes\delta(\omega)##, I should integrate $$\int_{-\infty}^\infty \delta(\omega-\Omega)\delta(\Omega) d\Omega$$ This integrand "fires" at two places: ##\Omega = 0## and...

Homework Statement [FONT=Courier New]If f(x)=|x-1/2|-5 determine g(x)=2f(-x+(3/2)) Homework Equations The Attempt at a Solution [FONT=Courier New]Well, I tried to factor out the k-value in the g(x) formula. So I was left with: g(x)=2f(-1)(x-3/2) Then I multiply f(x) by 2 and am left with...

Hi I am studying Differantial Geometry.My textbook is Lipschultz Differantia Geometry and I am in chapter two.I undersand the basic idea of Vector function but I wanI to gain more information.Is there any video lectures about vector functions.I found this...

What can be said about the arguments of the exponential functions and trig functions ? Can the argument be a vector or must it be a scalar ? If it can only be a scalar must it be dimensionless ?

Hi, I have the following equation: f(z)=g(z)+b*u(z) where z=(x,y) i.e. bivariate,b is a parameter, u(z) the uniform distribution and g(z) a function that represents distance. By considering for a momment b=0, min(f(z)) can give me the location of the minimum distance. However because I want...

Homework Statement f(x)=(√x^2-3x+2)/(2x-3), g(x)=3/(√(x+3)) and h(x)=(x^2-5x+6)/(x-2) which of the following are true: A)Df={x∈ℝ:x≤1 or x≥2} B)Dg={x∈ℝ:x≥-3} C)Dh=ℝ Homework EquationsThe Attempt at a Solution I am using substitution here by replacing the x by the parameters specified and...

Homework Statement f(x)=(√x2-3x+2)/(2x-3), g(x)=3/(√x+3) and h(x)=(x2-5x+6)/(x-2) which of the following are true: A)Df={x∈ℝ:x≤1 or x≥2} B)Dg={x∈ℝ:x≥-3} C)Dh=ℝ Homework EquationsThe Attempt at a Solution I am only attempting now,

Ok. I'm now studying economics and applied math, and I'm currently wanting to know what book or online resource could help me in learning how to model real life situations into functions. Most math and econ textbooks are garbage at this. I'll be more specific. In my study of Microeconomics...

I've been learning about Greens functions. I'm familiar with how to find them for different differential operators and situations but far from fully understanding them. We were shown in lecture how they can be used to obtain a perturbation series, leading to Feynman diagrams which represent...

Hello, I've been trying to come up with a short way of writing the code. What I'm trying to do is: I have 11 equations, each of which have a defined minimum and maximum. I'm trying to find the highest maximum out of all of them and I need to know which one it is. The highest as in farthest...

Can anyone explain how to solve a multiline function with two variables? Please see attached.

There are 2 trig functions on the same set of axis. f(x)=600sin(2π3(x−0.25))+1000 and f(x)=600sin(2π7(x))+500 How do I go about finding the points of intersections of the two graphs? This was from a test I had recently and didn't do too well on,so any help would be much appreciated. I started...