1
vote
3answers
44 views

show that every rational number has one and only one multiplicative inverse

I am stumped and have no idea on how I prove this. I don't know what else to say. I am beyond lost.
0
votes
1answer
55 views

How to find the inverse of f?

$ f : A \rightarrow B $ where $ A = B = \left \{4,5,6,7 \right \} $ $ f = \left \{ (4,6),(5,5),(6,7),(7,5) \right \} $ Find $ f^{-1} $ I know how to find the inverse of $ f $ if it were ...
0
votes
1answer
33 views

Number of configurations in a constrained nested loops and configuration back from serial

Consider 4 counters looping the digits 0, 1, 2 to form the various "configurations", like in : ...
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 ...
0
votes
2answers
285 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 ...
1
vote
1answer
80 views

How would I show this bijection and also calculate its inverse of the function f?

I want to show that f(x) is bijective and calculate it's inverse. Let f (x) : R → R be defined by f (x) = (3x/5) + 7 I understand that a bijection must be injective and surjective but ...
2
votes
0answers
43 views

Ultrametric matrices and their inverse

A non-negative square matrix $A$ is ultrametric iff: $A(i,i)>\{A(i,k),A(k,i)\}\forall k,i$ $A(i,j)\geq\min\{A(i,k),A(k,j)\}\forall i,j,k$ It is well-known that the inverse of non-negative ...
-1
votes
3answers
83 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, ...
1
vote
3answers
873 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
372 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 ...
0
votes
1answer
169 views

Equivalence Relations with inverses?

I have no Ida how to approach this problem: Suppose S is a relation on a set X which is reflexive and transitive. Then S intersection S inverse is an equivalence relation on X. Any idea on how I ...