Inverse Definition and 1000 Threads

[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...

Homework Statement I need to prove that Q[√2,√3] = \{a+b√2+c√3+d√6: a, b, c, d \in Q\} is a field. Homework Equations The Attempt at a Solution I proved all axioms except the existence of inverses for nonzero elements. My problem is that multiplication is quite hairy. I ended up...

Homework Statement I have some problem finding the inverse laplace transformation of the function: \frac{s}{s^2+2s+5} Homework Equations http://math.fullerton.edu/mathews/c2003/laplacetransform/LaplaceTransformMod/Images/Table.12.2.jpg The Attempt at a Solution I tried to...

hey guys can you help solve this problem. $\displaystyle\int\frac{dx}{\sqrt{2x-x^2}}$ i know that i have to change the integrand into this form $\displaystyle\frac{du}{\sqrt{a^2-u^2}}$ can you please show me how. thanks!

Homework Statement I have that X is distributed with Gamma(a,b) and that Y = \frac{1}{X}. I found the pdf of Y to be \frac{1}{\Gamma(a)b^a} \left(\frac{1}{y}\right)^{a+1} e^{-1/yb} for y > 0. I need to use this to find the expected value. Homework Equations The gamma function is...

f(x)=(x^5)/x^2+6 and f(x)=2x^3-4x I tried x=(y^5)/(y^2+6) then x(y^2+6)=y^5 but idk after and y=2x^3-4x then idk what to do

Homework Statement The nonlinear, inherently unstable inverted pendulum is shown in Figure 1.15. The goal is to maintain the pendulum angle θ(t) = 0 by using a feedback controller with a sensor (encoder or poten- tiometer) for θ(t) and an actuator to produce an input force f (t). The...

Homework Statement I have two questions sin2x = 1/25 and this obviously becomes sinx= +-(1/5) I also have cos2-1.5cosx-0.54 and cosx = (-3/10) and (9/5) Now this is asking for me to solve for the x value in radians in the domain [0,2pi] and I have no idea how to solve these for exact values...

Homework Statement I'm stuck trying to find out the inverse Laplace of F(s) to get y(t) (the solution for the differential equation): Y(s) = 1 / [ (s-1)^2 + 1 ]^2 The Attempt at a Solution I tried using a translation theorem and then apply the sine formula, but the denominator...

Does every FFT have \(i\) in it? Given \(u_t = -(u_{xxx} + 6uu_x)\). \(f'''(x) = \mathcal{F}^{-1}\left[(ik)^3\mathcal{F}(f(x))\right]\) \(f'(x) = \mathcal{F}^{-1}\left[(ik)\mathcal{F}(f(x))\right]\) The only equation I have used the pseudo-spectral method on was the NLS which is \(u_t =...

Quoting from Wiki, bolded section mine: What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?

I need some help understanding inverse functions, we've had a 4-page chapter covering the basics of inverse functions and I understand that. But now we have suddenly gotten these task that I don't understand how to solve, I've read the part on inverses several times, but I still don't...

Within certain branches of analysis - both real and complex - the Inverse Tangent Integral (and its generalizations) can be quite useful. Similarly, it's much less well-known (= uglier? lol) cousin, the Inverse Sine Integral can be used to solve many problems. To that end, this is not really a...

1. Homework Statement A permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume s << r. a) Use the binomial approximation (1+x)-n ~= 1-nx if x << 1 to show that the net force exerted...

q)give the converse ,the contrapositive and inverse of these conditional statements a)if it rains today,then i will drive to work b)if |x|=x then x>=0 c)if n is greater than 3,then n^2 is greater then 9

i know when you are dealing with limits you can take the inverse to fit the standard limit equations. how about integrals? can u take the inverse for instance: integral(f(x)dx) turn it into integral((1/f(x))dx)^-1) get the answer and then reverse it back? when can u or can't you take...

1. Which of the following is a group? To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2. 2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted. 3. The question...

How does this work? I'm very confused about the phi is solved using inverse sin. knowing: A=(c^{2}_{1}+c^{2}_{2})^{1/2} and c_{2}= Acos(\phi) solve for \phi which yields: \phi=sin^{-1}\frac{c_{2}}{(c^{2}_{1}+c^{2}_{2})^{1/2}}=tan^{-1}\frac{c_{2}}{c_{1}} I'm not sure how we use the inverse...

Hi ! I've been thinking this problem a whole and I could not find an answer. I want to solve the following problem: suppose I have N mass particles with absolute coordinates \mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_N . Besides, I have the following contraints: for all i=1,2,\ldots,N-1...

Homework Statement Evaluate ∫(x^2-4)^(1/2) / x for x > 2 Homework Equations The Attempt at a Solution I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this...

Homework Statement The problem can be found in Jackson's book. An infinitesimal Lorentz transform and its inverse can be written under the form ##x^{'\alpha}=(\eta ^{\alpha \beta}+\epsilon ^{\alpha \beta})x_{\beta}## and ##x^\alpha = (\eta ^{\alpha \beta}+\epsilon ^{'\alpha \beta})...

Homework Statement I have to turn this homework in online... I just want someone to check my work Convert from Cartesian coordinates to Polar coordinates (-1,-sqrt(3)) if r > 0 and if r < 0. Homework Equations The Attempt at a Solution if r > 0 then I believe the answer is...

I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question. Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse...

hi all, I have a TEC data and I got this TEC = \intNe ds How can I inverse this equation to get data for Ne. Thank you

I know the inverse of a function is found in two steps. Isolate the independent variable and then switch the variables like this: [y = x^{3} +1] = [x = \sqrt[3]{y - 1}] Then switch the variables to get: y = \sqrt[3]{x-1} However, when it comes to finding the derivative of the...

f(x) where x belongs to all real numbers inverse: f-1(x), where x belongs to all real numbers True or False: The inverse of f(x+3) is f-1(x+3) My ideas: I think that it is false given that when you usually find the inverse of a function, you switch the x and y variables and solve for y again...

Homework Statement Find the inverse of f(x)=ln(x^3-3x^2+3x-1) Homework Equations n/a The Attempt at a Solution y=ln(x^3-3x^2+3x-1) x=ln(y^3-y^2+3y-1) e^x=(y^3-y^2+3y-1) i looked around for inverse of cubic functions and i found a monster of a formula...

Homework Statement Find the inverse Laplace transform of e^(-3pi*s)/(s^2+2s+3). Homework Equations I know that you're supposed to factor out the e^(-3pi*s) and the other part becomes 1/(s+1)^2+2 but how do you get the answer? I'm confused. The Attempt at a Solution The answer is...

Homework Statement Which of the following is the solution set of the equation $$2\arccos(x)=\text{arccot}\left(\frac{2x^2-1}{2x\sqrt{1-x^2}}\right)$$ A)(0,1) B)(-1,1)-{0} C)(-1,0) D)[-1,1] Ans: A Homework Equations The Attempt at a Solution I start by rewriting LHS in terms of ##\arctan##...

Homework Statement The sum of the infinite terms of the series \text{arccot}\left(1^2+\frac{3}{4}\right)+\text{arccot}\left(2^2+\frac{3}{4}\right)+\text{arccot}\left(3^2+\frac{3}{4}\right)+... is equal to A)arctan(1) B)arctan(2) C)arctan(3) D)arctan(4) Ans: B Homework Equations The Attempt at...

Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution

Homework Statement Find the Inverse Laplace Transform of \frac{1}{(s^{2} + 1)^{2}} Homework Equations The Attempt at a Solution I tried using partial fractions but it didn't work. It looks like a cosine transform, but I don't know what else to do. Help please :(

Homework Statement Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)). Homework Equations A/s+(Bs+C)/(s^2+4) 8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A 8=A+B C=-4 A=3 B=5 L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4)) =3+ (Now I'm stucked.) The Attempt...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) Part B 2) Given the functions f(X) = 7x^2 - 5x and g(x) = 2x - 3 determine and simplify the following: a) (f-g)(x) My Answer: 7x^2 - 7x - 3 b) (f - g)(2) My...