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

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Inverse or Not Inverse Matrices

Compute the products $\begin{bmatrix} a & b\\ c &d \end{bmatrix}\begin{bmatrix} d &-b \\ -c&a \end{bmatrix} and \begin{bmatrix} d &-b \\ -c& a \end{bmatrix}\begin{bmatrix} a & b\\ c &d \end{bmatrix}$ Show that when ad-bc= 0, A given by $(*)$ cannot…

inverse

asked Nov 17 '16 at 04:47

user6259845

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2 answers

Matrix without an inverse

Using the definition of an inverse, can someone explain why $0_n$$_x$$_n$ cannot have an inverse. Also can someone explain if AB=$0_n$$_x$$_n$ for two nxn nonzero matrices A and B, then how A nor B can have an inverse.

inverse

asked Nov 17 '16 at 03:46

user6259845

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2 answers

Why is the domain different on the inverse of this function?

I have the function $$f(x) = \frac{x}{x^2 - 1}$$ The domain of this function is $(-1,1)$ and the range is $\mathbb{R}$. When I find the inverse of this, this becomes $$f^{-1}(x) = \frac{1 + \sqrt{4x^2+1}}{2x}$$ The domain seems to be different, now…

inverse

asked Aug 25 '16 at 01:29

Trumpetplayer0098

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0 answers

Inverse of a function defined as an integral

I am trying to get the inverse of: $$g(x) = \int _a ^x h(t) dt$$ That is, I want to find a general expression for $g^{-1}(x)$ and was wondering whether there are theorems I can apply. Thanks

inverse

asked Aug 10 '16 at 18:25

splinter

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4 answers

How to find an inverse of the following function?

$$f(x)=x^3+1$$ To find inverse, from what I've learned we change the y to x $$x=y^3+1$$ solve for y $$x-1=y^3$$ Should I cube root the x-1 for this? if i did that I still would not get the answer that would match the answer choice given to me What…

inverse

asked Jun 05 '16 at 21:25

MATH ASKER

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1 answer

Knwing when the inverting operation were wrong with $A^{-1}A$ result

I don't know why but I'm really really weak in inverting matrices since years... I always do some mistakes. I'm asking you how could I cope with that problem and be able to invert matrix easily in the future. For instance I tried to calculate the…

inverse

asked May 04 '16 at 10:54

Revolucion for Monica

1,511

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1 answer

Find the inverse of $θ:P(\Bbb{Z})→P(\Bbb{Z})$ defined as $θ(X) = \bar X$

Find the inverse of $θ:P(\Bbb{Z})→P(\Bbb{Z})$ defined as $θ(X) = \bar X$ (the complement of $X$)? Would the inverse of the function just be the function itself?

inverse

asked Apr 27 '16 at 01:21

Emily

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2 answers

Inverse calculation

I am trying to project estimated internal resistance of a battery. We know that the internal resistance approximately halves as the capacity of the battery doubles. For example... A 2AmpHour cell has 8milliOhms of resistance A 4AmpHour cell has…

inverse

asked Mar 28 '16 at 02:30

Virt

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1 answer

inverse function for big 'x'

let be a function so $ f(x)= x^{2}+h(x) $ , here $h(x) $ is a function so $ h(x) = O(logx)$ it is clear that $ f(x) \sim x^{2} $ for big 'x' so the inverse $ f^{-1}(x)\sim x^{1/2}$ for big 'x' is this correct, does this mean that the function $…

inverse

asked Jul 11 '12 at 10:17

Jose Garcia

8,506

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2 answers

Proof that if gcd(e, φ(N)) > 1, then a multiplicative inverse does not exist.

I am attempting a two-part problem on proofs and I am stuck on the second part. I think I have answered the first part correctly. (Note: these proofs are RSA-related, hence the variables) Here is the first part with my answer: Prove that if…

inverse

asked Jan 04 '16 at 22:33

user9750060

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1 answer

Using inverses to find solutions.

So upon solving some trigonometric equations, I found myself using the following method often:$$f[g(x)]=h(x)$$$$f[g(g^{-1}(x))]=h[g^{-1}(x)]$$$$f(x)=h[g^{-1}(x)]$$Which is how I usually find $f(x)$ when another function is inside it. But is there a…

inverse

asked Dec 17 '15 at 00:14

Simply Beautiful Art

74,685

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0 answers

Show the inverse of the One to One function

Is anyone able to guide me in the right direction for this question. This is for a beginner assembly language class. This is an online course so I am unable to ask the professor for guidance. Show that the one to one function: $f^{-1}$ : $N_{10}…

inverse

asked Sep 08 '15 at 22:20

groot

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1 answer

Finding multiplicative inverse Euler's theroem

been struggling this whole day with trying to figure out the multiplicative inverse of 17 modulo 31 using Eulers theorem. We know that 31 is a prime, φ(n)=30, so i end up with 17^30=(cong)1 (mod 31). But how do proceed from this to get the inverse…

inverse

asked Aug 18 '15 at 14:47