If $f(g(g(f(x)))) = x$ then does $f(g(x)) = g(f(x))$? [closed]
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Let $S$ be a set and $f, g: S to S$ such that for all $x in S$, $f(g(g(f(x)))) = x$. Is it true that for all $x in S$, $f(g(x)) = g(f(x))$?
real-analysis
asked Dec 17 '18 at 1:57
user627084user627084
31
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closed as off-topic by Saad, Nosrati, RRL, Brahadeesh, user10354138 Dec 17 '18 at 5:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Nosrati, RRL, Brahadeesh, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
Let $S$ be a set and $f, g: S to S$ such that for all $x in S$, $f(g(g(f(x)))) = x$. Is it true that for all $x in S$, $f(g(x)) = g(f(x))$?
real-analysis
asked Dec 17 '18 at 1:57
user627084user627084
31
$endgroup$
closed as off-topic by Saad, Nosrati, RRL, Brahadeesh, user10354138 Dec 17 '18 at 5:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Nosrati, RRL, Brahadeesh, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $S$ be a set and $f, g: S to S$ such that for all $x in S$, $f(g(g(f(x)))) = x$. Is it true that for all $x in S$, $f(g(x)) = g(f(x))$?
real-analysis
asked Dec 17 '18 at 1:57
user627084user627084
31
$endgroup$
Let $S$ be a set and $f, g: S to S$ such that for all $x in S$, $f(g(g(f(x)))) = x$. Is it true that for all $x in S$, $f(g(x)) = g(f(x))$?
real-analysis
real-analysis
asked Dec 17 '18 at 1:57
user627084user627084
31
asked Dec 17 '18 at 1:57
user627084user627084
31
asked Dec 17 '18 at 1:57
user627084user627084
31
asked Dec 17 '18 at 1:57
user627084user627084
31
asked Dec 17 '18 at 1:57
user627084user627084
31
31
closed as off-topic by Saad, Nosrati, RRL, Brahadeesh, user10354138 Dec 17 '18 at 5:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Nosrati, RRL, Brahadeesh, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, Nosrati, RRL, Brahadeesh, user10354138 Dec 17 '18 at 5:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Nosrati, RRL, Brahadeesh, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
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Try $g(x) = -x$ and $f(x) = x/(x-1)$ (on a suitable $S$ where you won't end up dividing by $0$, e.g. the irrationals).
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Try $g(x) = -x$ and $f(x) = x/(x-1)$ (on a suitable $S$ where you won't end up dividing by $0$, e.g. the irrationals).
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
$endgroup$
add a comment |
$begingroup$
Try $g(x) = -x$ and $f(x) = x/(x-1)$ (on a suitable $S$ where you won't end up dividing by $0$, e.g. the irrationals).
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
$endgroup$
add a comment |
$begingroup$
Try $g(x) = -x$ and $f(x) = x/(x-1)$ (on a suitable $S$ where you won't end up dividing by $0$, e.g. the irrationals).
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
$endgroup$
Try $g(x) = -x$ and $f(x) = x/(x-1)$ (on a suitable $S$ where you won't end up dividing by $0$, e.g. the irrationals).
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
answered Dec 17 '18 at 2:05
Robert IsraelRobert Israel
327k23216469
327k23216469
add a comment |
add a comment |
