Tagged Questions
0
votes
0answers
18 views
Inverse Variation Function as Real Life Example
What is an example of the Inverse Variation in real life? Given the function y = a/x'. I've tried to Google it, and look in all our math books, but I can find no examples.
4
votes
3answers
133 views
How to find inverse of the function $f(x)=\sin(x)\ln(x)$
My friend asked me to solve it, but I can't.
If $f(x)=\sin(x)\ln(x)$, what is $f^{-1}(x)$?
I have no idea how to find the solution. I try to find
...
10
votes
5answers
358 views
What's the difference between arccos(x) and sec(x)
My question might sound dumb, but I don't really see why the graphics of arccos(x) and sec(x) are different, because as far as I know arccos is the inverse cosine function (cos(x)^-1) and sec equals ...
5
votes
2answers
57 views
Inverse and derivative of a function [duplicate]
Find an example of an inverse function f(x) such that its derivative is the same as its inverse.
I tried many different functions but non of them worked.
0
votes
2answers
55 views
correct name of mathematical property
I am developing a program that transforms artifacts in one (computer) language to artifacts in another language. In my program there are certain border line situations where the result of applyin the ...
2
votes
6answers
78 views
How should I understand $f^{-1}(E):=\{x\in A:f(x)\in E\}$?
I understand the concept, but I still can't figure out how to read the notation:
$$f^{-1}(E):=\{x\in A:f(x)\in E\}$$
I understood the concept due to the examples, not with the notation. Can someone ...
1
vote
2answers
35 views
question about inverse functions
Functions $f$ and $g$ are defined by
$$ f: x\mapsto 2x+1$$
$$g: x \mapsto \dfrac{2x +1}{x+3}$$
(i) Solve the equation $gf(x) = x $
(iii) Show that the equation $g^{-1} (x) = x$ has no ...
-1
votes
3answers
56 views
How to find the inverse of a function $f:\mathbb{Z}_{30}\to\mathbb{Z}_{30}$ defined by $f([a])=[7a]$
If $f:\mathbb{Z}_{30}\to\mathbb{Z}_{30}$ is a function defined by $f([a])=[7a]$, show that $f$ is one-to-one and onto, and find $f^{-1}$.
I've got proof that the function is well defined, one to one, ...
5
votes
2answers
98 views
Help finding inverse of $f(x)=\frac{e^x-e^{-x}}{2}$
I'm trying to find the inverse of $f(x)=\frac{e^x-e^{-x}}{2}$. My textbook says $f^{-1}(x)=\ln(x+\sqrt{x^2+1})$, but I haven't been able to get that answer. Switching $x$ and $y$, I tried solving for ...
6
votes
4answers
163 views
Proof: if the graphs of $y=f(x)$ and $y=f^{-1}(x)$ intersect, they do so on the line $y=x$
This came out of a textbook problem, and as Lubin pointed out below, it's not actually true as originally stated. I'm guessing it should be restated as: If the graphs of $y=f(x)$ and $y=f^{-1}(x)$ ...
1
vote
3answers
100 views
How to find the inverse of this exponential function?
Here is the function... It is $y=e^{x-3}+5$, I have no clue how to find the inverse of it. I graphed the function but now it says find the inverse and graph it. I do not know how to graph it.
0
votes
1answer
38 views
When is (a restriction of) the map $y = f(x) = x + \frac{n}{x}$ bijective, if $x, y \in \mathbb{Q}$ and $n \in {\mathbb{Z}}^{+} \cup \{0\}$?
A good day to everyone.
If $0 < x \in \mathbb{Q}$, $0 < y \in \mathbb{Q}$, $n \in {\mathbb{Z}}^{+} \cup \{0\}$, and $n$ is squarefree, then the function
$$y = f(x) = x + \frac{n}{x}$$
is not ...
0
votes
3answers
113 views
Inverse of sum of two functions
Assuming two functions are invertible, is it true that the inverse of the sum of the two functions is the sum of the inverses (assuming all functions are well behaved)?
1
vote
1answer
62 views
inverse of function
Thanks for the help! Here is the solution..
i had a problem:
$$f(x)=\frac{(\sqrt x+8)}{(5-\sqrt x)}$$
i had to find the inverse, so lets begin...
1) first i write in terms of $y$
...
2
votes
2answers
69 views
Inverse of inverse of function?
What is the inverse of inverse of a function (I assume the original function is invertible)? Is this the original function? Is it always true?
2
votes
3answers
261 views
The relation between an exponential function and a logarithmic function
I have been told multiple times that the logarithmic function is the inverse of the exponential function and vice versa. My question is; what are the implications of this? How can we see that they're ...
1
vote
1answer
56 views
Will SADMEP always work to evaluate the inverse of a function, and I should not evaluate right to left?
How do you evalulate $f^{-1}(5)$ where $f(x) = (3 + 2) - (x * 4)$
I understand that if $f(x) = y$ then $f^{-1}(y) = x$
The input and output are essentially reversed. The most common place I have ...
2
votes
1answer
42 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
84 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
63 views
A differentiable injective function with Lipschitzian Inverse
I'm having difficulty with the following question which was given to me following studying the inverse mapping theorem.
Let $U\subseteq\mathbb{R}^{n}$
be an open set and let $f:U\to\mathbb{R}^{n}$
...
1
vote
2answers
98 views
second derivative of the inverse function
I know that the derivative of the inverse function of $f(x)$ is $g'(y) = \frac{1}{f'(x)}$
But how to derive the formula for the second derivative of g(y) knowing that $[\frac{1}{f(x)}]' = ...
1
vote
1answer
720 views
Find inverse of polynomial function
Do you know how I could compute the inverse function of the following polynomial?
$f(x) = x^5+x^3+x$
Thanks in advance.
1
vote
3answers
67 views
What is the relation between two invertible functions
Lets say that if f(x) and g(x) are invertible.
1- is (f(x)+g(x)) also invertible?
2- is f(g(x)) invertible too?
for the first one lets say that
f(x)=x and g(x)=-x
then f(x)+g(x)=x+(-x)=0
and ...
0
votes
2answers
97 views
how to find two right-inverse functions of a function
i am stuck in this problem. i need to find two right-inverse functions of this function:
$h: \Bbb N_0\times \Bbb N \to \Bbb N, (m,n)\mapsto m+n$.
i know that the function h' is a right inverse of ...
0
votes
1answer
49 views
Inverse of a function
From my text book it says that $f(x)= x^3$ and $f^{-1}(x) = \sqrt[3]{x}$ , which I totally agree with.
why does $f(x)= 1/(x-1)$ and $f^{-1}(x)= 1/x + 1$ and not equal $f^{-1}(x)= 1/(x+1)$?
I know ...
1
vote
2answers
161 views
0
votes
0answers
141 views
How do we find the inverse of a function $f(m,n)$ if there is a constant k?
I know I need to use the inverse matrice, but the problem is (the parameter) $k$, because it's a variable that can take any value depending on $k$, but it's not a variable. Think of the derivative ...
2
votes
3answers
404 views
How do we find the inverse of a function with $2$ variables?
$$f(m,n) = (2m+n, m+2n)$$
What do we have to do to find the inverse of this function?
I don't even know where to begin.
1
vote
3answers
81 views
Is the inverse of a function the reflection of the function about the line $y=x$?
So if we have
$f(x)$:
$y=x$ when $x \ne 1$ and
$y = 0$ when $x = 1$.
The inverse would be:
$y=x$ when $x \ne 0$ and
$y=1$ when $x = 0$
?
3
votes
3answers
192 views
How to invert this function? (Inverse exponential function with arctan)
How to invert this function?
$$
y = e^{\arctan(x^5)}
$$
0
votes
2answers
414 views
How to find the inverse to $f(x)= x^2 - 6x + 11 $
If the inverse exists, how do I find the inverse to this function:
$$
f(x)= x^2 - 6x + 11
$$
with $x \le 3$
Stuck at the quadtric formula. I think i have got the right answer which is $x = 3 ± ...
1
vote
0answers
39 views
Looking for correct terminology
Given the functions $f\colon A\to B$ and $g\colon B\to B$, a common, useful strategy is to define a new function $h\colon A\to A$ as the composition $f^{-1}\circ g\circ f$.
There seem to be many ...
0
votes
1answer
41 views
How is it simplified?
1 ) I have this equation and don't know how $(1 + 2e^y)$ and $(1 + 2e^x)$ from each side of equation cancelled each other out and get the final answer $x = y$.
...
1
vote
1answer
57 views
Conditions on function inverses
I have recently asked a question related to an inverse function which was not so obvious to calculate:
Inverse function of $y=W(e^{ax+b})-W(e^{cx+d})+zx$
Now I would like to learn;
Given ...
5
votes
3answers
274 views
Inverse function of $y=W(e^{ax+b})-W(e^{cx+d})+zx$
I have a simple question for which I am looking for a closed form expression (If there exits one). In other words, given:
$$y=W(e^{ax+b})-W(e^{cx+d})+zx$$
where $W$ is the Lambert $W$ function and ...
5
votes
6answers
271 views
What is the inverse function of $\ x^2+x$?
I think the title says it all; I'm looking for the inverse function of $\ x^2+x$, and I have no idea how to do it. I thought maybe you could use the quadratic equation or something. I would be ...
3
votes
1answer
63 views
Find whether or not an inverse exists algebraically
Is there an algebraic(without graphs) way to determine the existence of a function's inverse without using calculus?
I'm an undergrad engineer and can obviously solve this using basic calculus, but ...
1
vote
3answers
612 views
Prove $ \sqrt{\arctan(x)} = (1/2) \arccos((1-x)/(1+x))$
$$ \sqrt{\arctan(x)} = \dfrac{1}{2} \arccos\left(\dfrac{1-x}{1+x}\right)$$
I have been trying to solve this problem for the past hour, but I'm not able to solve it as I have just started solving ...
2
votes
2answers
160 views
Write the above function in simplest form.
$$\tan^{-1}\left(\dfrac{3a^2x-x^3}{a^3-3ax^2}\right),\;a>0;\; -\frac{a}{\sqrt{3}}\leqslant x \leqslant \frac{a}{\sqrt{3}}$$
Hi,
Please help me to solve this problem. As I can solve simple ...
1
vote
1answer
182 views
Write the following functions in simplest form.
$$ \arctan\left(\frac{x}{\sqrt{a^2-x^2}}\right)$$
Hi,
I am not able to solve this problem from last 1 hour. Please help me to solve this question.
As I can solve simple inverse ...
2
votes
3answers
293 views
Simplify $\tan^{-1}[(\cos x - \sin x)/(\cos x + \sin x)]$
Write the following functions in simplest form:
$$\tan^{-1}\left(\frac{\cos(x)-\sin(x)}{\cos(x)+\sin(x)}\right), \quad 0<x<\pi$$
Please help me to solve this problem. I have been trying ...
2
votes
3answers
145 views
Inverse function requirements
Let f be an injective function, that is:
$f : X \rightarrow Y$
$f(a) = f(b) \implies a = b$
Now, my question is, does the following need to hold in order for function to be injective:
$(\forall x ...
0
votes
2answers
72 views
Searching for a suitable invertible function
I am searching for a monotonically increasing and invertible function in $2$ variables. I know several monotonically increasing functions. This is also true for invertible functions. But I am ...
3
votes
3answers
140 views
Finding the inverse function, is there a technique?
I came across a way to find whether some number is inside a sequence of numbers.
For example the sequence (simple function for positive odd numbers):
$$a(n) = 2n + 1.$$
So the numbers inside it go: ...
1
vote
1answer
96 views
generalised inverse function
Let $f:\mathbb{R} \rightarrow [0, 1]$ be increasing (edit: i.e., non-decreasing).
Define $f^-(y) = \inf \{x \in \mathbb{R} : f(x) \geq y \}$, $y \in [0, 1]$.
Is the following line true?
$$x \leq ...
1
vote
1answer
62 views
Invert “Gravitational” Force Function or Solve an Intersection
Recall "gravitational"-type force functions, by which I mean anything of the form:
$f(x,y,z) = \frac{k}{((x-x_0)^2+(y-y_0)^2+(z-z_0)^2)^p}, p\in\Re_{>0}, k\in\Re, (x,y,z) \neq(x_0,y_0,z_0)$
(e.g., ...
0
votes
4answers
477 views
Finding the inverse of $h(x) = 3^x$
most of the time I know how to find the inverse of a function (make it equal $y$, solve for $x$ and then swap $x$ and $y$), but I have no idea how to do that for this one, so any help would be great: ...
0
votes
2answers
521 views
Proving a Composition of Functions is Bijective
If I have $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f$ is onto and $f\circ f\circ f = f$, how can I prove that $f$ is bijective? I know that I only have to prove that it is 1-to-1 because I'm ...
1
vote
1answer
335 views
Does there exist an inverse function for this summation?
Given the formula $\sum_1^n{i} = \frac{n ( n - 1)}{2} $, does there exist a function $F$ such that $F(n) = i$?
If so, what is it? If not, why not?
2
votes
1answer
180 views
Differentiate an Inverse Function, Two Methods?
I would like to take the derivative of this inverse function at $\pi$: $f(x) = 2x + \cos{x}$, given that ${f}^{-1}(\pi) = \frac{\pi}{2}$.
I know that there are two methods of doing it. Let me ...
