Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [inverse]

Inverses include: multiplicative inverse of a number (reciprocal), inverse function, matrix inverse, etc. A subject tag such as (linear-algebra), (algebra-precalculus) or (arithmetic) should be added to clarify in which sense "inverse" is used. This tag should never be the only tag on a question.

An inverse is an operation that reverses the effect of another operation. This is a broad concept that arises in many areas of mathematics.

  • Multiplicative inverse: $2^{-1} = 1/2$
  • Inverse function: $\sin^{-1}x$ is the inverse of sine
  • Inverse matrix $A^{-1}$
  • Left and right inverses of group elements, of operators between linear spaces, etc.
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Inverse function -- need help

I'm a senior software developer but my math lessons are a bit rusty. I know the name of what I want, but not anymore how to compute it ;) I've found (by myself with Grapher.app) a simple easing function (for transitions), that's a bijection from…
Cyrille
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Inverting matrix with an identity row

By identity row, I mean a row in a square matrix that that has 0s everywhere except for a 1 in the n-th column. When you invert an NxN matrix with an identity row, does the inverted matrix always preserve the number of zeros (N-1) for that specific…
24n8
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inverse of a function and its differentiable

I want to prove that this function $f(x)=\frac{x}{\cos x}$ from $(-1,1)$ to $\mathbb R$ is bijective? whether or not has an inverse differentiable? I know that this function is injective and surjective so is bijective, but I am not able to find its…
zeinab
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Find inverse of exponential function

Do you know how I could compute the inverse function of the following exponential sentence? $$y=\dfrac{e^x}{1+2e^x}$$
Diego Pacheco
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Inverse of sum of identity matrix and a special matrix

How to calculate the inverse of the matrix $(I_{m+1}+A)$, where $A$ is given by $ \[ A=\left( \begin{array}{cc} 0 & a1_{m}^{T} \\ a1_{m} & 1_{m}1_{m}^{T}% \end{array}% \right) , % $ with $1_{m}$ is a vector of ones of length $m$, $I_{m}$ is an…
Charles Chou
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showing a matrix has an inverse and how it is constructed from that matrix

Can someone explain how you would do these problems, I understand what inverses are, but I really don't understand these problems. B)Suppose that $A$ is $50\times 50$ and that $A^3-2A^2+9A+7I_{50}=0_{n\times n}$. Show that $A$ must have an inverse…
user6259845
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Inverse Z transform of $\dfrac{2(z^2-5z+6.5)}{(z-2)(z-3)}$, for $2<\left|z\right|<3$

I want to find inverse $\mathcal{Z}$ transform of $\dfrac{2(z^2-5z+6.5)}{(z-2)(z-3)}$ valid on an annulus region for example for $2<\left|z\right|<3$
Rag
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Find the inverse function of $y=x|x|e^x$

I am having problems finding the inverse function of a complicated function. In this case: $$y=x|x|e^x $$ I thought I could 'split' this function but I'm not sure if that's the right way. for $y=x$ it would be $x=y$ for $y=e^x$ it would be…
sophie
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What is $\ln(e^x -4) $, solving for the inverse?

What is $\ln(e^x -4) $, solving for the inverse? I know $\ln(e^x)$ is just $x$, but I don't know what to do with the 4.
user310160
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If f(x+y)=f(x)*f(y) and f is a bijection, show that its inverse satisfies this function equation

I'm having trouble with this problem. I'm not even sure how to go about finding the inverse of an equation with both x and y. Here is the problem: If $f(x+y)=f(x)*f(y)$ and $f$ is a bijection, show that its inverse satisfies the functional…
Emma
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Finding the inverse of a function using bisection method

It is said that we can find $f^{-1}(y)$ by solving the equation $y-f(x)=0$ using bisection method. But all sources that I can find use bisection to find roots, so I can't figure how and why. Could you explain it?
user137035
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Flip Values to get the opposite

Not sure of the name of what I need to do, but I used to do it all the time, and now i forget. I have values 1 - 10. I want 10 to become 1 and 1 to become 10. What is the formula to do this again? It is driving me nuts. Thanks for the responses. My…
D_C
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Verify if 2 functions are inverse to each other

According this site, 2 functions $f$ and $g$ are the inverse function of each other, only if both $(f \circ g) (x) = x$ and $(g \circ f) (x) = x$ are true. Is it really necessary to prove both of them? Can someone please provide an counter example…
Fermat's Little Student
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how to do inverse laplace of $(s^2+1)/s^4$?

how to do the inverse laplace of $(s^2+1)/s^4$? the answer is $(t^3/6)+t$ but I do not know how to derive it.
zee
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If I have two functions defined from $\mathbb{R^3} \to \mathbb{R}$, can they be inverses?

I am taking an economics class and I am not getting some straight answers about the conditions under which I can say that a map from $$\Bbb{R}^3 \rightarrow \Bbb{R}$$ can be reduced to a map from $$\Bbb{R} \rightarrow \Bbb{R}$$ Specifically, I have…
Stan Shunpike
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