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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 cubic centimeter to inverse cubic meter

If I have $x$ $ cm^{-3}$, how can I convert it to $y$ $ m^{-3}$? What is $y$ in terms of $x$?
WantsToLearn
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Get the Standard Inverse using Moore-Penrose Inverse

I need to find the standard inverse of a large n*n matrix N (n=1,000,000). I know that N*R=B and I have the matrix B, of the shape (n,k) (k=1,000). I have the Moore-Penrose Inverse of matrix R (n,k). I multiplied the B and the inverted R, and got a…
dbank04
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Is $[\sin(1/2)]^{-1}$ identical to $\frac{1}{\sin(1/2)}$

I'm in Grade 12 Advanced Functions and having some trouble with understanding the difference between $\sin^{-1}(1/2)$ and $(\sin(1/2))^{-1}$. I recognize that the former asks to find an angle whose sine is 1/2, and the latter is just a…
arara
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Inverse function of 2D-circle: f(u,v,a) = (x,y,r)

Can someone explain to me, how I can get $f^{-1}(x,y,r)=\begin{bmatrix}u\\v\\a\end{bmatrix}$ Someone told me to look into the inverse function theorem, but I only have high-school education, I know the basics, but looking into wikipedia and youtube…
theHeavyLobster
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Inverse function to f

I have function f : $\mathbb{R}$ → $\mathbb{R}$ defined by f(x) = $e^{-3x}-3e^{-2x}$ and have found that f'(x)=$-3e^{-3x}+6e^{-2x}$. Can someone explain why f does not have an inverse function. And how can I find the largest interval I that…
Fork
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The inverse of $A+O(N^{-1})$

Assume $A$ is invertible and I want to calculate $(A+O(N^{-1}))^{-1}$ I want to know if there exist any formula for it? $O(N^{-1})$ is the big $O$ notation. That is the inverse of an invertible matrix $A$ plus some matrix which converge to $0$ as…
ANuo
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Does the usage of Principal value branch for range in inverse trig function is correct?

Does the Usage of expression " Principal value branch" for range in the Inverse trigonometric function is correct? Does it imply range of inverse trigonometric function?
KUGVE H VASUDEVA
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Help with restricted domain of a function to find inverse

Restrict the domain of $f(x)$ to find inverse: \begin{align} f(x) & = x^2+6x+9 = (x+3)^2 \\ g(x) & = \sqrt{x} - 3 \end{align}
glue
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The fastest method of finding the inverse of a 1024 bit number (N) i.e. 1/N?

I have been trying to find inverses of large integers (could be upto 2048 bits), such that 1/N has a minimal period p and n its length in binary. (what i actually am interested in finding is the length of the minimal period n) Now could someone…
Malik Hamza Murtaza
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Bijective Inverse function

http://prntscr.com/h3mlga http://prntscr.com/h3mlpj Hey guys could someone check my inverse question? would be highly appreciated, if theres anything i could do to improve the layout would be great too many thanks. Thanks in advance :) p.s sorry…
Mathlete
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Inversly proportional theory

Let's begin our discussion: Many people find that time seems to pass more quickly as you get older. So, the older you are, the shorter a year seems. Let's model this experience mathematically. Let's theorize that your perception of a length of time…
Edgar
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Inverse of exponential function

How can I find the inverse of $3^{5^{x}}$ ? I tried using logarithm in base 3: $3^{5^{y}}=x \Longrightarrow \log_3x=5^y \Longrightarrow \log_5(\log_3x)=y$? Is it correct? in my book it says its another answer from those given so I can't know the…
Lola
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Can we define inverse function for the injections?

My calculus book denotes like following: If $f: X \rightarrow Y$ is injective $ \Rightarrow$ $f^{-1}$ is defined as following : $f^{-1}(b) = a \iff f(a) =b$ where domain of $f^{-1}$ is $Y$ and codomain is $X$ But What I know is inverse exists only…
Daschin
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Inverse of non-continuous scale

I'm currently struggling with inverting a value on the non-continuous scale -2 0 1 5 to a value on the following (inverted) scale 5 1 0 -2 What I tried before is the commonly suggested approach of value = maxOfScale + minOfScale - value but…
raphael
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Stuck on the inverse of a function

I am stuck in trying to inverse this function: $f(x) = x-(x-0.75)^2+a\ln((x-0.75)^2+1)$ Where $x\in(0.75;1.25)$. Does anybody has an idea of the solution? Is there a method you advice? I tried on wolfram alpha, but it is not finding any…
Du Bois Eloi
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