# Tagged Questions

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.

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### Inverse function to $f(t)=3t+4ln(t+1)=y$

I have to invert the function $f(t)=3t+4\ln(t+1)=y$, so $f^{-1}(y)=t$. But I am struggling to invert this. Is there a solution?
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### Prove $sgn(π) = sgn(π^{-1})$?

I'm pretty sure the inversion count of $π$ should be the opposite of the inversion count of $π^{-1}$. By this I mean if $π$ looks like this: $1 \to 1$, $2\to 2, \ldots, 10 \to 10$ and therefore the ...
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### Simplifying Inverse Trig Function

I'm trying to figure out how to simplify this expression but I'm not quite sure on how to approach this question. How should I approach this question? Any help is greatly appreciated! ...
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### Show that a matrix satisfying certain conditions is non-singular

I have a square matrix $A$ satisfying the following conditions: The elements on the diagonal are negative; All other elements are non-negative; All row sums are less than or equal to $0$; There is ...
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### I need someone to show me how to solve this input/output problem

Alright, so I have: $4y^3 = x$ And now I have to solve for $y$, where I can later use that equation to answer other questions I have. Can someone hint me out on how to solve for $y$ given the above ...
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### The existance of Schur Complement Inverse

A block matrix $\mathbf{M}=\left[ \begin{array}{ccc} \mathbf{A} & \mathbf{B} \\ \mathbf{B}^T & \mathbf{C} \end{array} \right]$ is invertible if $\mathbf{A}$ and ...
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### Is the inverse of a real, continuous “1-1” function necessarily continuous itself? [closed]

If so, please do provide me with an epsilon-delta proof, if possible. Thanks in advance.
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### Inverse of the sum of a invertible matrix with known Cholesky-decomposion and diagonal matrix

I want to ask a question about invertible matrix. Suppose there is a $n\times n$ symmetric and invertible matrix $M$, and we know its Cholesky decomposion as $M=LL'$. Then do we have an efficient way ...
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### Is a regular stochastic matrix definitely nonsingular?

Is a regular stochastic matrix definitely nonsingular (invertible)? How to prove it ? It says here that 'For a regular matrix always an inverse matrix exists' ...
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### Inverse Trig Functions Composite functions of Csc, Sec, And Cot

Ok guys.. I'm trying to get prepared for my test tomorrow and I did numerous exercises. But I stumbled upon one of the "types" of exercises. Which is a composite function in $\csc$ and $\sec$. For ...
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### Matlab function for finding matrix inverse with cayley hamilton theory

I want to write function in matlab that would calculate the inverse of a matrix using its trace. I know that there are other ways to calculate the inverse but I need it to be with trace. I couldn't ...
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