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
1
vote
1 answer

Prove that scalar functions of vectors cannot be inverted

The following seems obvious to me (because information is clearly lost), but I have no idea how to prove it: Suppose we have some arbitrary complex vector $\mathbf{A}$ with $m$ components. Let $f(\mathbf{A}):\mathbb{C}^{m}\rightarrow\mathbb{C}$.…
SDiv
  • 2,520
0
votes
1 answer

conditions for Gauss_jordan elimination with no pivoting

Please note that here is Gauss_jordan elimination which help us get inverse of A. I am wondering, is there any condition that it could work without pivoting? I try to prove this under column diagonally dominant, but I could pass one step in my…
airbender
  • 13
0
votes
2 answers

How to find the inverse system of a given one

what is the inverse formula of y[n]=x[n]*x[n+1] ? And how can I find the inverse formula/system of a given one in general? I'm having some troubles with this when it comes to some formulas.
user144550
  • 3
0
votes
1 answer

Finding inverse using logs

$$ x = \left(\frac{4^y}{-2}\right)^{\frac{1}{3}} $$ i have correct answer of $\:y=\log(4)-2x^3$ i'm lost on steps to obtain the answer. i tried the…
user118512
  • 101
0
votes
3 answers

How to find inverse of...

How do you find the inverse of the equation in the form $y= b^{x-h} +K$ for example: $y=2^{x-4} +6$ I already know that the inverse of $b^x$ is $\log_bx$ but how do you find with the $H$ and $K$ value included?
Hunter
  • 1
0
votes
3 answers

Inverting this equation as a function of $x$

I'm trying to inverse this equation as a function of $x$ $$z = x + \frac{x^2}{2}$$ but couldn't wrap up my head around it. If anyone can provide a step by step solution to this it will be really helpful. Thanks in advance!
clinraus
  • 3
  • 1
0
votes
1 answer

Left inverse of function $f:\mathbb R \to \mathbb R$

Let there be a function $f: \mathbb R \to \mathbb R$ given by $$f(x)=\begin{cases}5x + 2&x\geq 1\\x-1&x<1 \end{cases}$$ Give an example of a Left inverse of $f$, and prove that it is correct. I can do this with normal function. But how does this…
arieenhenk
  • 51
0
votes
0 answers

How do I show that g ◦ f = id, when I only have the information that f is injective?

Let f ∈ Hom(R3,R7) be an injective map, then there exists a g ∈ Hom(im(f), R3 ) such that g ◦ f = id. We have that invertibility is equivalent to injectivity and surjectivity. But how do I show that g ◦ f = id, when I only have the information that…
Marie
  • 1
0
votes
2 answers

Evaluate $\sin[\pi/2-\sin^{-1} (-1/2)]$

My answer isn't even in options. What am I doing wrong?
Dingus45191
  • 179
0
votes
0 answers

$\lim_{x\to 0}\frac{\arcsin x}{x}=1$

I am trying to show that $$\lim_{x\to 0}\dfrac{\arcsin x}{x}=1$$ I am new to inverse trigonometric functions, so I am sorry if it's obvious. So if we put $\arcsin x=t,$ then $\sin t=x$. How do I say where t goes when $x\to 0$?
Trifon
  • 113
0
votes
1 answer

Finding the Inverse of a 5th order Function

I need to get the inverse of that function. Can I get some help please? Thanks! $$ f(x) = -x^5-2x+2 $$
Alex
  • 337
0
votes
1 answer

$y=\ln \cos x$ inverse function flawed

The Domain of $f(x)$ is $(0,1)$. When finding the domain of $f(\ln(x))$ We can say: $0<\ln x<1$ and apply the inverse $\ln$ function $\exp$. We get $e^0 < e^{\ln(x)} < e^1$ which leads to $1
queency3 jones
  • 1
0
votes
1 answer

Does there exist an inverse for an exponential difference/addition?

does the inverse of the following function exist? If not (as said by many calculators), I'd like to know why, plotting it in desmos seems to show it is one-to-one. $$f(x)=9^x-e^x$$ I found a similar question from 7 years ago, Inverse Function of…
Gabriel Sánchez
  • 1
0
votes
1 answer

Creating Inverse Function with Certain Characteristics

Given the following: $D : \in \Re [-n, n]$ $R: \in \Re[-\frac\pi4, \frac\pi4]$ The curve of the function should be completely smooth, and can be undefined outside the given Domain. The graph should be symmetrical across $y = -x$ $f^{-1}(f(x)) = x$…
gardian06
  • 221
0
votes
0 answers

Finding inverse of a sixth order tensor

I'm working on finding the inverse (triple contraction) of a sixth-order tensor, in which each index is an integer ranging from $0$ to $2$ so it has $729$ elements in total. The sixth-order tensor has the totally symmetry, $$\LARGE…
William Chan
  • 1
1 2 3
4
5 6 7 8