# Tagged Questions

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### How to find the inverse of the function?

$$f(x)=\frac{x+2}{5x-1}$$ Answer: $$f^{-1}(x)=\frac{x+2}{5x-1}$$ Can one of you explain how the inverse is the same exact thing as the original equation?
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### Finding the inverse of $f(x)=|x|-2$

How would I find the inverse of the function $f(x)=|x|-2$? I have swapped $x$ and $y$, and tried to isolate $y$, reaching up to $x+2=|y|$ Whenever I see absolute values, I always break the problem up ...
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### Find the inverse of $f(x) = (x+1)/(x-8)$

Find the inverse of this function: I have gotten this far: $x = y+1/y-8$ $x(y-8) = y+1$ $x(y-8)-1=y$ $xy-8x - 1 = y$ I think I went backwards?
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### Inverse function (basic algbra math)

Consider the following function: $f(x) = {1 / (x-6) }$ Find a formula for the inverse of the function. Here is what have so far? $y = 1/(x-6)$ ---> $x = 1/(y-6)$ But my embarrassing problem is ...
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### Find the inverse of a function.

$$g:[-1,1] \to \mathbb R\\ g(x)={\frac{x}{x+2}}$$ $f:[-1,1] \to$ range of f. Find the inverse of $f.$ $\forall y\in \text{range of }g$ there exist some ${\frac{2y}{1-y}}\in [-1,1]$ such that ...
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### Primes and Inverses of an integer

I have the following question which I do not understand. Here it is: Consider the primes $5$, $7$ and $11$ as n. For each integer from $1$ through $n - 1$, calculate its inverse. I do not ...
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### Is the pseudoinverse of a singular, lower triangular matrix itself lower triangular?

Suppose $L\in\mathbb{R}^{n\times n}$ is a singular, lower triangular matrix. Is its psuedoinverse, $L^\dagger\in\mathbb{n\times n}$, also lower triangular? I have already proved by induction that the ...
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### Implicit Function Theorem to show no function can be one to one

Apply Implicit Function Theorem to show that no $C^1$ function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ can be one to one near any point of its domain. Repeat the proof by using Inverse Mapping Theorem ...
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### Apply Implicit Function Theorem

Apply Implicit Function Theorem to show that no $C^1$ function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ can be one to one near any point of its domain. Repeat the proof by using Inverse Mapping Theorem ...
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### What is the inverse of this function?

please help me to find out the inverse this function, $$f(x)=\frac{e^x+e^{-x}}{e^x-e^{-x}}$$ I know that, let $$y=\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}$$ and if I find $x=\cdots$ then that is the ...
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To save me some time writing everything out in latex, I'm adding a picture of the question and Ill try to explain what I understand for the problem. Just a heads up, I'm really not sure how to do this ...
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### Finding the integral of an inverse cosine function?

I've just been having trouble with this question: "Differentiate $xcos^{-1}x$ and hence find the integral of $cos^{-1}x$. Hint: Try using the substitution $u=1-x^2$." Finding the derivative wasn't ...
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### Expressing an inverse trig function?

I just need a little help with this question: "Express cos$y$ in terms of cos $y/2$ and hence show that tan$^{-1} sqrt[(1-x)/(1+x)] = 1/2$ cos$^{-1}x$, for $0<x<1$." I can do the first part, ...
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### Inverse of $f(x) = 18sin(\frac{x\pi}{7})+20$

This is an exercise taken from Mooculus-textbook (page 17, exercise 5 to be exact). The task given is to find an inverse for $f(x) = 18\sin(\frac{x\pi}{7})+20$ (restricting domain to $[3.5,10.5]$) ...
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### Inverse Z transformation in specific points

I'm given $$H(z)=\frac{z^4+6z}{z^6+1}$$ and I need to find $h(k)$ for $k=0,1,2,3,4$. Where $H(z)$ is the Z transformation of $h(k)$. Since H is very complicated, I believe some trick could be ...
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### Inverse Z transformation of 1/(z^2(z^2+1)^2)

I need to find the inverse Z transformation of $\frac{1}{z^2(z^2+1)^2}$ So far, I've tried using the convolution property, and so, inverting $\frac{1}{z(z^2+1)}$, gave me $-0.5i({{(-i)}^k-i^k})$ for ...
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### Calculate inverse modulo: $8^{-13}\pmod {29}$

How can I calculate $8^{-13}\pmod{29}$ ? I don't get how it works. Can I do it separately? So first $8^{-13}$ and then modulo $29$. And how can I calculate a negative power the quickest?
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### The differentiability class of the inverse function

Here's the final part of a proof (from Marden's Elementary Classical Analysis) of the inverse function theorem, where we have been given that $f$ is of class $C^p$: Could someone please explain the ...
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### Finding inverse of a matrix

This question is in my assignment. We are not allowed to use any symbol to represent any elementary row and column operations used in the solution. We must solve it step-by-step. Please help me to ...
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### Finding the inverse function

The question is to find the inverse function of $$f(x)=x-(2\sqrt{x})+1$$ I first found that the domain of definition is $\,x\ge 0$ Then studied the variation of the function and it is decreasing ...
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### Inverse functions and tangent line

Let $f(x) = \frac14x^3 + 12x + 6$ and let $y = f^{-1}(x)$ be the inverse function of $f$. Determine the $x$-coordinates of the two points on the graph of the inverse function where the tangent line is ...
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### Sufficient to show that $\sinh(\operatorname{arcsinh}(x))=x$ for arcsinh being the inverse of sinh?

I have to show that arcsinh is the inverse function to sinh. I checked that $\sinh(\operatorname{arcsinh}(x))=x$. Is that sufficient or do I also need to show that ...