Is there something wrong with brackets? $f(2x+(f(y)+f(f(y))=4x+8y$ [closed]
$begingroup$
$ x,y inmathbb{R}$ and $f:mathbb{R} rightarrow mathbb{R}$, find a function that,
$$f(2x+(f(y)+f(f(y))=4x+8y$$
A) $f(x)=2^x$
B) $f(x)=2x$
C) $f(x)=2^x-3$
D) $f(x)=2x^2-3$
E) $f(x)=4x-2$
My problem is,it seems to me that there's something wrong with brackets. Or do I think wrong?
algebra-precalculus contest-math problem-solving
asked Jan 5 at 11:02
ElementaryElementary
360211
$endgroup$
closed as off-topic by Nosrati, Leucippus, user91500, Paul Frost, Abcd Jan 6 at 13:09
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." – Nosrati, Leucippus, user91500, Paul Frost, Abcd
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
$ x,y inmathbb{R}$ and $f:mathbb{R} rightarrow mathbb{R}$, find a function that,
$$f(2x+(f(y)+f(f(y))=4x+8y$$
A) $f(x)=2^x$
B) $f(x)=2x$
C) $f(x)=2^x-3$
D) $f(x)=2x^2-3$
E) $f(x)=4x-2$
My problem is,it seems to me that there's something wrong with brackets. Or do I think wrong?
algebra-precalculus contest-math problem-solving
asked Jan 5 at 11:02
ElementaryElementary
360211
$endgroup$
closed as off-topic by Nosrati, Leucippus, user91500, Paul Frost, Abcd Jan 6 at 13:09
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." – Nosrati, Leucippus, user91500, Paul Frost, Abcd
If this question can be reworded to fit the rules in the help center, please edit the question.
5
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
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It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15
add a comment |
$begingroup$
$ x,y inmathbb{R}$ and $f:mathbb{R} rightarrow mathbb{R}$, find a function that,
$$f(2x+(f(y)+f(f(y))=4x+8y$$
A) $f(x)=2^x$
B) $f(x)=2x$
C) $f(x)=2^x-3$
D) $f(x)=2x^2-3$
E) $f(x)=4x-2$
My problem is,it seems to me that there's something wrong with brackets. Or do I think wrong?
algebra-precalculus contest-math problem-solving
asked Jan 5 at 11:02
ElementaryElementary
360211
$endgroup$
$ x,y inmathbb{R}$ and $f:mathbb{R} rightarrow mathbb{R}$, find a function that,
$$f(2x+(f(y)+f(f(y))=4x+8y$$
A) $f(x)=2^x$
B) $f(x)=2x$
C) $f(x)=2^x-3$
D) $f(x)=2x^2-3$
E) $f(x)=4x-2$
My problem is,it seems to me that there's something wrong with brackets. Or do I think wrong?
algebra-precalculus contest-math problem-solving
algebra-precalculus contest-math problem-solving
asked Jan 5 at 11:02
ElementaryElementary
360211
asked Jan 5 at 11:02
ElementaryElementary
360211
edited Jan 5 at 11:47
Elementary
asked Jan 5 at 11:02
ElementaryElementary
360211
asked Jan 5 at 11:02
ElementaryElementary
360211
asked Jan 5 at 11:02
ElementaryElementary
360211
360211
closed as off-topic by Nosrati, Leucippus, user91500, Paul Frost, Abcd Jan 6 at 13:09
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." – Nosrati, Leucippus, user91500, Paul Frost, Abcd
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Nosrati, Leucippus, user91500, Paul Frost, Abcd Jan 6 at 13:09
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." – Nosrati, Leucippus, user91500, Paul Frost, Abcd
If this question can be reworded to fit the rules in the help center, please edit the question.
5
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
$begingroup$
It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15
add a comment |
5
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
$begingroup$
It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15
5
5
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
$begingroup$
It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Looks like the red parenthesis is superfluous: $$f(2x+color{red}{(}f(y)+f(f(y))=4x+8y$$
since $$f(y)+f(f(y)) = color{red}{(}f(y)color{red}{)}+f(f(y)) = color{red}{(}f(y)+f(f(y))color{red}{)},$$
so let us just ignore it.
That leaves us with three cases:
- $f(2xcolor{blue}{)}+f(y)+f(f(y))=4x+8y$
- $f(2x+f(y)color{blue}{)}+f(f(y))=4x+8y$
- $f(2x+f(y)+f(f(y))color{blue}{)}=4x+8y$
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
$endgroup$
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Looks like the red parenthesis is superfluous: $$f(2x+color{red}{(}f(y)+f(f(y))=4x+8y$$
since $$f(y)+f(f(y)) = color{red}{(}f(y)color{red}{)}+f(f(y)) = color{red}{(}f(y)+f(f(y))color{red}{)},$$
so let us just ignore it.
That leaves us with three cases:
- $f(2xcolor{blue}{)}+f(y)+f(f(y))=4x+8y$
- $f(2x+f(y)color{blue}{)}+f(f(y))=4x+8y$
- $f(2x+f(y)+f(f(y))color{blue}{)}=4x+8y$
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
$endgroup$
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
add a comment |
$begingroup$
Looks like the red parenthesis is superfluous: $$f(2x+color{red}{(}f(y)+f(f(y))=4x+8y$$
since $$f(y)+f(f(y)) = color{red}{(}f(y)color{red}{)}+f(f(y)) = color{red}{(}f(y)+f(f(y))color{red}{)},$$
so let us just ignore it.
That leaves us with three cases:
- $f(2xcolor{blue}{)}+f(y)+f(f(y))=4x+8y$
- $f(2x+f(y)color{blue}{)}+f(f(y))=4x+8y$
- $f(2x+f(y)+f(f(y))color{blue}{)}=4x+8y$
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
$endgroup$
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
add a comment |
$begingroup$
Looks like the red parenthesis is superfluous: $$f(2x+color{red}{(}f(y)+f(f(y))=4x+8y$$
since $$f(y)+f(f(y)) = color{red}{(}f(y)color{red}{)}+f(f(y)) = color{red}{(}f(y)+f(f(y))color{red}{)},$$
so let us just ignore it.
That leaves us with three cases:
- $f(2xcolor{blue}{)}+f(y)+f(f(y))=4x+8y$
- $f(2x+f(y)color{blue}{)}+f(f(y))=4x+8y$
- $f(2x+f(y)+f(f(y))color{blue}{)}=4x+8y$
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
$endgroup$
Looks like the red parenthesis is superfluous: $$f(2x+color{red}{(}f(y)+f(f(y))=4x+8y$$
since $$f(y)+f(f(y)) = color{red}{(}f(y)color{red}{)}+f(f(y)) = color{red}{(}f(y)+f(f(y))color{red}{)},$$
so let us just ignore it.
That leaves us with three cases:
- $f(2xcolor{blue}{)}+f(y)+f(f(y))=4x+8y$
- $f(2x+f(y)color{blue}{)}+f(f(y))=4x+8y$
- $f(2x+f(y)+f(f(y))color{blue}{)}=4x+8y$
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
answered Jan 5 at 11:35
EnnarEnnar
14.7k32445
14.7k32445
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
add a comment |
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
1
1
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
$begingroup$
(+1) By the way thank you for not saying the answer. I'll solve it myself according to your correction.
$endgroup$
– Elementary
Jan 5 at 11:43
1
1
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
@Beginner, you are welcome. If you are doing this for practice, I would still try the other two options as well. It might help you see why some of the proposed solutions cannot work, no matter the parentheses.
$endgroup$
– Ennar
Jan 5 at 11:48
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
$begingroup$
+1. Perfectly well explained.
$endgroup$
– Lucas Henrique
Jan 5 at 12:40
add a comment |
5
$begingroup$
Yes: the number of left ones does not match the number of right ones. But it is enough to add the two missing right parentheses.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 11:04
$begingroup$
I think two more parentheses should be added
$endgroup$
– Mostafa Ayaz
Jan 5 at 11:14
$begingroup$
It's not unamibiguous, though, is it @MauroALLEGRANZA ?
$endgroup$
– ancientmathematician
Jan 5 at 11:14
$begingroup$
@MauroALLEGRANZA Doing what you say, are you sure that question can be fixed only in one version?
$endgroup$
– Elementary
Jan 5 at 11:15