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.
4444 questions
0
votes
1 answer

How do I find an inverse for this injective multivariate function?

I have come up with an injective multivariate function that puts out a unique value for every configuration of four positive natural numbers provided that $\omega\ge\psi\ge\chi\ge\theta\ge1$ $f(\omega,\psi,\chi,\theta)=…
Leaven
  • 1
0
votes
1 answer

I need help finding the inverse of this formula

So basically I’m trying find the inverse to this formula and I’m having trouble getting it could anyone help me out I would appreciate it thank you $$f_{3t}(x) = \frac{\log(25-(-1.8(x)))}{\log(x)}$$ edit: to clarify I am under the assumption that…
SelfProclaimedDev
  • 326
0
votes
0 answers

how to invert the following function?

I am trying to invert the function below with respect to $w$ but in vain. Can you show me how ? $$m[w,x] = sgn[x]|x|^w$$ where $w\geq 0, x \in [-1,1]$, which results in $m[w,x] \in [-1,1]$ I am not sure if below is the correct answer ? $$w = sgn(x)…
user1769197
  • 1,227
0
votes
1 answer

Inverse of sum of inverse matrices

My method needs to solve the following problem. $$A = (B^{-1} + C^{-1} - D^{-1})^{-1}$$ Is there any way to rewrite this to avoid "too much" matrix inverse when implementing this in python? The matrices are all symmetric and positive.
Gunhild
  • 1
0
votes
1 answer

Inverse function $f(x) = 3^x$

$f(x) = 3^x$ find $x $ when $f^{-1}(x) = 4$ $y = 3^x$ $x=log_{3}(y)$ $\therefore f^{-1}(x) = log_{3}(x)$ $4= log_{3}(x)$ $x = 3^4$ $x = 81$ simple solution but I was helping my little brother with his o level past paper and the answer they had was…
Tariro Manyika
  • 111
0
votes
1 answer

Is it possible to find the inverse to this function?

Sorry if this is not a good question, but I normally don't venture to the math side of things, at least not that far where I can't stand anymore, so please forgive me if this question is not well formulated. I was wondering if it is possible to find…
Feirell
  • 53
0
votes
0 answers

Inverse Clarification

I just learned Inverse Variation. I'm a bit confused with it but I need some clarification. Is it the same as inverse functions and numbers? For example, $0.1 = 10$. Is the Inverse Variation what I think it is?
Blade
  • 5
0
votes
1 answer

How do you find the inverse of $\ -log(\frac{x}{y})$?

There's this equation in chemistry called the hasselbalch equation. I looked at how it was derived, and it isn't making sense to me. $\ pKa -log(\frac{x}{y})$ equals to $\ pKa + log(\frac{y}{x})$, which confuses me because I thought the inverse…
Redwood
  • 167
0
votes
2 answers

What's the exact/closest approximate to the inverse of getting 70%?

To clarify: I'm creating a computer program and I'm trying to find the actual mathematical way of approaching my problem. Given a number x, a is 0.7x. After doing some testing, it seems that to get back up to x from a, I can multiply by 1.42857143,…
Emily
  • 11
0
votes
1 answer

inverse of the sum of a diagonal and a symmetric matrix

I need to compute the inverse of the following sum of matrices: $$\begin{pmatrix} 0 & B \\ B^T & 0 \end{pmatrix} +D $$ where B is a non-negative matrix and D is a non-negative diagonal matrix. They are both real an square matrices.
Sebastiano Della Lena
  • 11
0
votes
0 answers

What is the inverse of $f(x )= x \operatorname e^{|x|}$?

The function $$f(x )= x \operatorname e^{|x|} $$has an interesting semi-sigmoid shape. However, it is somehow a "horizontal" sigmoid. I would like to know the function of the vertical equivalent. So what is the inverse of this function?
Holgersson Måns
  • 1
0
votes
2 answers

is $f(x) = 2^x$ bijective?

I've been posed with the question "Why is $f$ not invertible?" I have learned that $x^2$ is not bijective unless I restrict it to only use non-negative Reals. However when I look at the curve of $2^x$ it looks to me that it passes the 1 unique x…
RyBoneCoder
  • 105
0
votes
1 answer

Solving inverse function equations

A function f is defined by $f(x) = \displaystyle\frac{2x-3}{x-1}, x≠1$. Solve the equation |$f^{-1}(x)$| = 1 + $f$-1$(x)$. I first found out the inverse and equated for the left hand side the negative of the inverse and then solved. However, I got…
V11
  • 95
  • 2
  • 9
0
votes
0 answers

Inversion in Mathematics

In what ways are students in grades 7-12 exposed to the mathematical concept of "inverse?" The few I've thought of are inverse operations and finding the inverse of a function. Any others?
Jack Esposito
  • 1
0
votes
3 answers

diagonal matrix and invertible matrix proof

I am given the following proof question: Let $A \in {\mathbb R}^{n\times n} $.` Show that there exist invertible matrices $B$, $C$ such that $A=B+C$. I believe it has something to do with diagonal matrix, but maybe I am wrong. thank you for the…
ga as
  • 21
1 2 3 4
5
6 7 8