Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [function-and-relation-composition]

For questions about the composition of functions and relations.

For questions about the composition of functions and relations: If $f\colon A\to B$ and $g\colon B\to C$ are functions, their composition $g\circ f\colon A\to C$ is given by $x\mapsto g(f(x))$. Similarly for $R\subseteq A\times B$ and $S\subseteq B\times C$ the composite relation is defined $S\circ R=\{(a,c); (\exists b\in B) (a,b)\in R \land (b,c)\in S\}$.

1202 questions
0
votes
1 answer

Which composition of functions is the right one?

This question seems a bit stupid but I am really confused: Let $f$ be a function and $g(z):=f(z)-f(2z)$. What is $g(-1/z)$? Is it $f(-1/z)-f(-2/z)$ or $f(z)-f(-1/(2z))$? Thank you!
user363705
0
votes
2 answers

$f \circ f^{-1} = i_B$ proof using the fact that $f^{-1} \circ f = i_A$

Suppose f is function from A to B, and suppose that $f^{-1}$ is a function from B to A. Assume $f^{-1} \circ f = i_A$. Then show therefore that $f \circ f^{-1} = i_B$. I tried applying left composition of $f^{-1}$ and right composition of $f$ to…
Ariana
  • 1
-1
votes
1 answer

Figuring out function composition

If I know $f(x)$ and $f(g(x))$, how do I figure out what is $g(x)$? I can solve already some simple cases, but I'm looking for a general strategy. Particularly in harder cases when just trying to figure it out is hard.
Anonymous
  • 1
-1
votes
2 answers

Commuting functions

I encountered the following exercice: Suppose $f$ is a quadratic function of the form $f(x)=ax^2+b$ with $a\neq 0$. Show that if $g(x)=c x^2+d$ with $c\neq 0$ is another function commuting with $f$ then $f(x)=g(x)$ for all $x$. Starting with the…
Dimitris
  • 767
-1
votes
1 answer

Composition of function $f (x) = \sqrt{2x^2+17}-3$ a total of $10$ times

So I have this question here. Obviously, I don't think I am expected to take a composition of a function 10 times. That would be crazy. My idea is that f(x) repeats 10 times and that $\sqrt{2}$ repeats 10 times too so I was thinking I could write…
Future Math person
  • 2,885
-2
votes
2 answers

Is composition of reversible functions reversible too?

This sounds obvious. Too obvious for me to be able to prove it formally. Can you please help with a formal proof of this?
ferdinandutkin
  • 1
-2
votes
1 answer

Given $f: \Bbb Z \to \Bbb Z$ defined by $f(x) = ax + b$, find the condition on $a,b$ that let $f \circ f = id_ \Bbb Z$.

Let $f:\Bbb Z\to \Bbb Z$ be defined by $f(x) = ax+b$, where $a, b$ are integers. Find the necessary and sufficient condition on $a, b$ in order that $f \circ f = id_\Bbb Z$ I can get the answer easily in a similar case where $f(x)=ax$, simply by…
Tom
  • 31
-2
votes
1 answer

How to find $g(x)$, if: $f(x)=(x+1)/x$, and $f(g(x))=x$?

How to find $g(x)$, if: $f(x)=\frac{(x+1)}{x}$, and $f(g(x))=x$? I know that the answer is that $g(x)=\frac{1}{(x-1)}$ But how to come to that answer remains a mystery to me Please give me some good advice Thanks in advance :)
Phillip Andreas Karlsen
  • 1
1 2 3 4
5