Inverse Definition and 1000 Threads

Hello all I was doing some approximation to solve another problem, but got stuck when trying to figure out a suitable inverse functions for this: a = \frac{\cos x}{3x^2 - \pi^2}, where 0 \le x \le \pi. What I need is the two functions x(a) at least near a \approx -0.086 \pm 0.01 but I'm not...

If f(x) = x^5 + x^3 + x, find f^-1 (3). I know we have to set the function equal to 3, and solve for x, but I don't think you can simplify the right side. Any help?

Homework Statement Proof that: f has an inverse ##\iff## f is a bijection Homework Equations /definitions[/B] A) ##f: X \rightarrow Y## If there is a function ##g: Y \rightarrow X## for which ##f \circ g = f(g(x)) = i_Y## and ##g \circ f = g(f(x)) = i_X##, then ##g## is the inverse...

Hello, I'm having trouble going about dealing with this question. It asked to find the inverse of the function and evaluate it at a certain number: Also for part b, do we just plug in x=11 and then take the inverse of that output value or what? I tried using some inverse properties: f^-1(x)...

Find the derivative of the function $f(y)$ $$f(y)=\tan^{-1}\left({8{y}^{3}+1}\right)$$

So, I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields? I think not because in order to not have a Flux depending on distance but a constant one we need that r^2 of the...

Homework Statement Let f(x) = 1−3x−2x^2 , x ∈ [−2, −1]. Use the Horizontal Line Test to show that f is 1–1 (on its given domain), and find the range R of f. Then find an expression for the inverse function f −1 : R → [−2, −1]. The Attempt at a Solution I have already done the horizontal line...

F has the following sets: F = {(1,3)(2,2)(3,2)(4,2)(5,5)} Does F^-1 mean: F = {(1,2)(2,2)(3,2)(4,5)(5,3)} Thank you.

As the denominator is a function of s + 3, it suggests a shift had to have been utilised. As such, we also need the numerator to be a function of s + 3... Let $\displaystyle \begin{align*} u = s + 3 \end{align*}$, then $\displaystyle \begin{align*} s = u-3 \end{align*}$ and thus...

Allo, When I was experimenting with graphing functions, I noticed the inverse tangent, or arctanget, curves away from y=2, or may be less. What is the y limit for the inverse tangent function? Does it for ever increase, or terminate at a co-ordinate?

It's not entirely obvious what to do with this question, as the denominator does not easily factorise. However, if we realize that $\displaystyle \begin{align*} s^4 + 40\,000 = \left( s^2 \right) ^2 + 200^2 \end{align*}$ it's possible to do a sneaky completion of the square... $\displaystyle...

Hi - I'm trying to figure out the specific steps in a math textbook. I'm trying to figure out how the textbook did its algebra here with a quadratic formula to find an inverse of a function: Sadly there's a step I'm supposed to know by now in the simplification algebra in there 3 steps...

Hi all! I know that the integral is the inverse of the derivative, but what about special derivative operators? What functions would undo the gradient, divergence and curl? And what about special integrals, such as line and surface integrals? Are there different derivatives/integrals that are...

I am interested in mini magnetospheres. How do i calculate the intensity of the field at a certain distance if i already know theits intensity at the source?

the volume of a sphere: V=(4/3)pi*r3 To me it looks like it is direct variation with a power function (V/r3=(4/3)*pi)but i don't think that's what they're looking for

Hi, I have a a Fourier transformed variable \hat{\eta}(k) defined as the following: \hat{\eta}(k)=\frac{e^{-k^{2}}\tanh k}{kU^{2}+(-B+\Omega U+E_{b}|k|-k^{2})\tanh k} The parameters U,B,\Omega,E_{b} have all been defined previously. I have naively tried the following: \eta...

Hello! Please, help me to see my mistake - for quite a while I can't solve a very easy matrix. I have to find the inverse of the given matrix using their determinants and adjoints. 4 6 -3 3 4 -3 1 2 6 to find adjoint matrix I need to find cofactors 11, 12, etc till 33. Cofactor11 =...

I am faced with the following question: Two point charges X and Y, exert a force F on each other when they are at a distance d apart (x and y are opposite charges). When the distance between them is 20mm, the force exerted on each other is 0.5F. What is the distance d? I know that, e.g...

w,8.7.8 nmh{925} $\displaystyle\int\frac{1}{\left(25-{t}^{2 }\right)^{3 /2 } }\ dt =\frac{t}{25\sqrt{25-{t}^{2 }}}+C$ $\begin{align}\displaystyle t& = {5\sin\left({u}\right)} & dt&={5\cos\left({u}\right)} du& \end{align}$ Then $...

Hi, What is the inverse of f(x)= e^x + e^-x +1?

Homework Statement F = k(Q2*Q1)/(r^2) Homework EquationsThe Attempt at a Solution I asked my teacher and he said that this is an inverse square law. Didn't say anything else. He also mentioned k is constant. I assume i can plug in random values and see if there is a pattern... k=1 for all Set...

Im having a problem with the inverse gamers fallacy. I can't get my heard round two seemingly true but contradictory statements. The original form of the fallacy as I understand it says that if you walk into a casino and see two 6's has been thrown on the table. That event is unlikely...

I noticed the graphs of ##y=\cos^{-1}x## and ##y=\cosh^{-1}x## are similar in the sense that the real part of one is the imaginary part of the other. This is true except when ##x<-1## where the imaginary part of ##y=\cos^{-1}x## is negative but the real part of ##y=\cosh^{-1}x## is positive. I...

Consider ##y=\cos{-x}=\cos x=\cosh ix##. Thus, ##\pm x=\cos^{-1}y## and ##ix=\cosh^{-1}y##. So ##\cosh^{-1}y=\pm i\cos^{-1}y##. Renaming the variable ##y##, we have ##\cosh^{-1}x=\pm i\cos^{-1}x##. Next, we evaluate the derivative of ##\cosh^{-1}x## by converting it to ##\cos^{-1}x## using...

Homework Statement After having struggled yesterday with this as much as I could, I am posting this problem here- if ##ax+bsec(tan^{-1}x)=c## and ##ay+bsec(tan^{-1}y)=c##, then prove that ##\frac{x+y}{1-xy}=\frac{2ac}{a^2-c^2}##.Homework EquationsThe Attempt at a Solution My attempt-...

Please take a look in below image. How do they get 2y = x + 2?

Homework Statement The problem- if $$\theta= tan^{-1}(\frac{a(a+b+c)}{bc})+tan^{-1}(\frac{b(a+b+c)}{ac})+tan^{-1}(\frac{c(a+b+c)}{ab})$$ , then find $$tan\theta$$ Homework EquationsThe Attempt at a Solution I tried to use these as sides of a triangle and use their properties, but other than...

Homework Statement Express $$ 2 arctan (\sqrt\frac{a-b}{a+b} tan (\theta/2))$$ in terms of inverse cosine Homework Equations I realize it amounts to find a smart substitution, but I can't find one. The Attempt at a Solution I tried ##b/a=tan \theta## , but I can't find any way to get rid of...

Homework Statement Solution set of the inequality (cot-1(x))2 -(5 cot-1(x)) +6 >0 is? Homework EquationsThe Attempt at a Solution Subs cot-1(x)=y We get a quadratic inequality in y. y2-5y+6>0 (y-2)(y-3)>0 Using the wavy curve method, the solution set is...

I'm trying to find the distribution of a random variable ##T## supported on ##[t_1, t_2]## subject to ## \mathbb{E}[V(t', T)] = K, \forall t' \in [t_1, t_2]##. In integral form, this is : $$ \int_{t_1}^{t_2} V(t', t).f(t) \, dt = K,\forall t' \in [t_1, t_2], $$ which is just an exotic integral...

Homework Statement If 1/2<=x<=1 , then cos-1[ x/2 + (√(3-3x2))/2] + cos-1 x is equal to? Homework EquationsThe Attempt at a Solution Substituting x=cosθ = cos-1(cosθ) + cos-1 [ cos(θ)/2 + (√(3(1-cos2(θ)))/2] = θ + cos-1 [cos (π/3) cos θ + sin (π/3) sinθ] =...

Please guide why answers are different in following two cases and which one is correct? Case 1. sin-1 ( – 1/2 ) – sin-1 (– 1) = 7π/6 – 3π/2 = – π/3 Case 2. sin-1 ( – 1/2 ) – sin-1 (– 1) = – sin-1 ( 1/2 ) + sin-1 (1)...

What test can we perform on a vector field to determine if there exist vector field(s) that describe its inverse curl?

Homework Statement Given the Laplace transform $$F_L(s) = \frac{1}{(s+2)(s^2+4)},$$ by using the complex inversion formula compute the inverse Laplace transform, ##f(t),## for the following regions of convergence: (i) ##Re(s)<-2;## (ii) ##-2<Re(s)<0;## (iii) ##Re(s)>0.## Homework Equations...

I've been trying to wrap my head around the relationship between temperature increase of an object at a distance and temperature of a heat source. From what I've found, the temperature increase of an object from thermal radiation is affected by the inverse square law...

Homework Statement Given the transformations ##x^2+y^2=2*r*cos(theta)## and ##x*y=r*sin(theta)## prove the Jacobian explicitly The question then goes on to ask how r and theta are related to the cylindrical coordinates rho and phi. I think ##r=1/2*(x^2+y^2)## and hence ##r=1/2 rho## but I am...

Hello all, I'm just doing some practice for an upcoming exam and came upon this question in my notes: One experimental way to generate very high energy photons is to ”collide” a laser beam against an electron beam, the photons that recoil in the direction parallel to the electron beam will have...

Homework Statement I'm actually a tutor, and a student has shown me one of their assignments. I think there's a notation error, I'm quite confident there is actually, but I don't want to assert this, or have my student go asserting it, without some more certainty. This is the question...

How would you go about doing this, I see it so often quoted as a method, but no-where can I find an example This is what I was thinking D=P^(-1)AP Would it then follow that D^(-1)=P^(-1)A^(-1)P ? My reasoning being: DD^(-1)= P^(-1)APP^(-1)A^(-1)P identity matrix= P^(-1)AA^(-1)P=identity...

I Am Wanting to Find out who Created the inverse square law.

T(t) = Ts+(98.6 – Ts)e-kt rewrite in the form t=g-1(T) In trying to understand how to find the inverse of this but am having a hard time, please advise. Thanks, Kupkake303

Hi there. I'm starting to work on diffuse optical tomography, and I need to introduce my self to the theory of inverse problems, and the different techniques to solve inverse problems, specially in the area I'm going to work, or things related to the inverse problems in electromagnetic theory...

My question is what inverse kinematics is. Many scientists are using inverse kinematics for measuring cross-section or something. For example, suppose that we measure cross section of 14N+p->n+14O. We can use N14 for beam and p for target. But, we can also do the other way. When they use...

I already googled this but I did not find a definite answer. Is there such a thing as a 'inverse riemann'? Specifically, where you invert the start number to be at the top of the riemann symbol and then decrement down to the end value which is on the bottom of the riemann symbol?

Hey! :o Let $R$ be a ring and $I$ the set of non-invertible elements of $R$. If $(I,+)$ is an additive subgroup of $(R,+)$, then show that $I$ is an ideal of $R$ and so $R$ is local. I have done the following: Let $a\in I$ and $r\in R$. We suppose that $ar$ is invertible, then...

Homework Statement Find the work done by the three-dimensional inverse-square field ## F(r) = \frac {1} {||r||^3} r ## on a particle that moves along the line segment from P(6, 2, 3) to Q(4,2,4) Homework Equations ## \int_C F \bullet dr = \int_a^b f(h(t), g(t)) \sqrt {(\frac {dx} {dt})^2 +...

Suppose ##v_i## is an eigenvector of ##A## with eigenvalue ##\lambda_i## and multiplicity ##1##. ##AA^{-1}v_i=A^{-1}Av_i=A^{-1}\lambda_iv_i=\lambda_iA^{-1}v_i## Thus ##A^{-1}v_i## is also an eigenvector of ##A## with the same eigenvalue ##\lambda_i##. Since the multiplicity of ##\lambda_i##...

I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained? I found this below from here, but could not really...

I'm trying to visualize the effect of the inverse square law, not on a direct source of light, but on scattered light carrying visual data, such as that responsible for our everyday sight of things as well as our images of Earth from satellites. It seems to me that it should be true that, while...

Homework Statement I need to prove that if ##f: \mathbb{R} \rightarrow \mathbb{R}## then the following two statements are NOT equivalent: 1) For every ##E \subset \mathbb{R}## that is Lebesgue-measurable, ##f^{-1}(E)## is Lebesgue-measurable. 2) For every ##E \subset \mathbb{R}## that is...