2
votes
7answers
588 views

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?
2
votes
4answers
73 views

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 ...
2
votes
2answers
55 views

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?
1
vote
2answers
27 views

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 ...
2
votes
1answer
42 views

How to find the inverse of this particular symmetric matrix

Basically, I have a $n \times n$ symmetric matrix, which looks like this: $$ \begin{bmatrix} 1 & \alpha & \cdots & \alpha \\ \alpha & 1 & \cdots &\alpha \\ \vdots &\vdots ...
1
vote
2answers
78 views

Derivatives of component inverse functions

I might have missed the point of the following questions. Anyone kindly give a suggestion? Let $f:\mathbb{R}_\mathbf{x}^3\to\mathbb{R}_\mathbf{y}^3$ and ...
1
vote
1answer
116 views

Finding the derivatives of inverse functions at given point of c

Hoping someone can help me the understand the steps to solve a problem like this. I'm guessing it involves the formula: $\frac{d}{dx}f^{-1}(f(x))=1/f'(x)$. Am I right in this assumption? I would post ...
1
vote
1answer
87 views

Inverse function theorem question - multivariable calculus

This is an exercise in Inverse Function Theorem http://en.wikipedia.org/wiki/Inverse_function_theorem we are given the function $f:\mathbb R^2 \to \mathbb R^2$, $f(x,y)=(e^x \cos y,e^x \sin y)$ 1) ...
0
votes
2answers
53 views

Find the range of arcsin$((1-x^2)^{0.5})$

Title says it all, how do you get the answer to this? So far I only reach $0<1-x^2<pi/2$ but I get an invalid answer from here. the correct answer is $0<x<pi/2$. Any help is appreciated, ...
-1
votes
4answers
26 views

Prove Inverse Function [closed]

Consider the function $f:\Bbb R\times\Bbb R→\Bbb R\times\Bbb R$ defined by $$f(x,y)=(x+y,x-y)$$ This function is invertible. Show that the inverse function is given by $$f^{-1} (a,b)=\left( ...
1
vote
2answers
45 views

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 ...
0
votes
2answers
47 views

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 ...
2
votes
0answers
64 views

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 ...
2
votes
1answer
116 views

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 ...
2
votes
1answer
99 views

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 ...
1
vote
2answers
75 views

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 ...
0
votes
2answers
179 views

Can someone please help with my inverse function and sets discrete math problem?

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 ...
0
votes
1answer
29 views

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 ...
1
vote
1answer
44 views

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, ...
0
votes
2answers
68 views

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 $[3.5,10.5]$) ...
0
votes
1answer
67 views

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 ...
0
votes
0answers
41 views

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 ...
0
votes
1answer
26 views

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?
0
votes
1answer
40 views

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 ...
3
votes
3answers
115 views

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 ...
1
vote
1answer
88 views

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 ...
0
votes
2answers
177 views

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 ...
1
vote
1answer
57 views

Computing the inverse Laplace transform of this?

What's the correct way to go about computing the Inverse Laplace transform of this? $$\frac{-2s + 1}{(s^2+2s+5)}$$ I Completed the square on the bottom but what do you do now? $$\frac{-2s + ...
3
votes
3answers
873 views

How do I find the inverse function of a polynomial with $x^5$?

I've been stumped on this problem for hours and cannot figure out how to do it from tons of tutorials. Please note: This is an intro to calculus, so we haven't learned derivatives or anything too ...
3
votes
1answer
95 views

Inverse of a polynomial function

I want to find the inverse of $f(x)=\frac{3}{4}x^2-\frac{1}{4}x^3 $ when $0<x<2$. According to wolfram the answer is inverse I would like to know how can I find wolfram's inverse.
1
vote
2answers
129 views

inverse of laplace transform

How to compute this inverse Laplace transform ? $$\displaystyle{ \mathcal{L^{-1}} \left\{ \frac{1}{s(\exp(s)+1)} \right\} }$$ Thanks.
8
votes
6answers
2k views

If $A^2$ is invertible, then $A$ is also invertible?

True or False: If $A^2$ is invertible, then $A$ is also invertible. ($A$ is a matrix here.) The answer is true. I was trying to come up with an example that makes this false. But I couldn't. ...
2
votes
1answer
56 views

Proof that an inverse of a possibly noncomputable function is possibly not decidable

I'm stuck with the following homework: Given an fixed function $f:\mathbb{N}\to\mathbb{N}$. $f$ is an arbitrary (possibly not computable, possibly partial) function. Show that the set $\{f(42)\}$ is ...
1
vote
2answers
108 views

What does this syntax mean: “$f^{-1} : N_{10} \Rightarrow N_b $ is the inverse of $f: N N_{b} \Rightarrow N_{10}$?”

I'm trying to solve this but I haven't seen syntax like this before. Can someone please explain the syntax? http://i.imgur.com/GO1Ki.png The image is Show that the one-to-one function $f^{-1} : ...
1
vote
1answer
615 views

Help with restricted domain of a function to find inverse [closed]

Restrict the domain of $f(x)$ to find inverse: \begin{align} f(x) & = x^2+6x+9 = (x+3)^2 \\ g(x) & = \sqrt{x} - 3 \end{align}
2
votes
0answers
340 views

Multivariable Inverse Function problem

Consider the system of equations $$\left\{\begin{align*} &x^5 v^2 + 2y^3 u = 3\\ &3yu - xu v^3 = 2\;. \end{align*}\right.$$ Show that near the point $(x,y,u,v) = (1,1,1,1)$, this system ...
1
vote
3answers
784 views

Finding The Equivalence Class

Okay, so the question I am working on is, "Suppose that A is a nonempty set, and $f$ is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs $(x, y)$ such ...
1
vote
0answers
112 views

How does adding extra row and column of ones affect a matrix's inverse?

I'm working on a homework problem, and I'm stuck. I guess my linear algebra still needs some work... I've arrived at $\mathbf{D}= \left[ \begin{matrix} \mathbf{C} & \mathbf{1}^T \\ \mathbf{1} ...
1
vote
4answers
320 views

What is the Inverse function of $f(x)=192x-16x^2$?

What is the inverse function of: $$f(x)=192x-16x^{2}$$ I have been finding myself going in a circle in trying to complete this problem which otherwise looks simple, but for some reason I am at a ...
2
votes
3answers
132 views

Determine invertible and inverses in $(\mathbb Z_8, \ast)$

Let $\ast$ be defined in $\mathbb Z_8$ as follows: $$\begin{aligned} a \ast b = a +b+2ab\end{aligned}$$ Determine all the invertible elements in $(\mathbb Z_8, \ast)$ and determine, if possibile, ...
0
votes
1answer
248 views

Identity element, invertible and inverse elements in $(\mathbb Z_7 \times \mathbb Z_{10}, \odot)$

Let $T=\mathbb Z_7 \times \mathbb Z_{10}$ and let $\odot$ be the operation defined as follows: $$\begin{aligned} (a,b)\odot(c,d) = (2+a+c, 3bd)\end{aligned}$$ Find the identity element, the inverse ...
1
vote
1answer
274 views

Prove inequality with norms and matrices

Prove that if $A$ is invertible and $||A-B||<||A^{-1}||^{-1}$ then $$\lVert A^{-1} - B^{-1}\rVert \leq \lVert A^{-1}\rVert \frac{\lVert I-A^{-1}B\rVert}{1-\lVert I-A^{-1}B\rVert}.$$ I also need ...
0
votes
0answers
110 views

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 ...