Functional equations and Determination of Function [on hold]

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Question
Find all (if any) functions $f$ taking the non-negative reals onto the
non-negative reals, such that

(a) $f(x(f(y))cdot f(y)= f(x + y)$ for all non-negative $x, y$;

(b) $f(2)=0$;

(c) $f(x)$ is not equal to $0$ for every $x$ belongs to $[0,2)$.

My process is shown in the image in the attachment.
Please suggest what can I further do to get the result. Also suggest if you have any other method for the question.

algebra-precalculus

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edited Aug 3 at 6:20

user529760

509216

asked Jul 31 at 18:18

jayant98

94

put on hold as off-topic by amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco Aug 5 at 7:10

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I don't think the title is appropriate. Functional analysis is something different.
  – Rumpelstiltskin
  Jul 31 at 18:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Then what it should be?
  – jayant98
  Jul 31 at 18:22
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Functional equations. Other than that, questions should ask one thing at a time.
  – Rumpelstiltskin
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is the topic of so-called "functional equations", I would change the title to reflect that.
  – Nico
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @jayant98 Why did you roll back my MathJax edit?
  – packetpacket
  Aug 1 at 19:36
  
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

1

Question
Find all (if any) functions $f$ taking the non-negative reals onto the
non-negative reals, such that

(a) $f(x(f(y))cdot f(y)= f(x + y)$ for all non-negative $x, y$;

(b) $f(2)=0$;

(c) $f(x)$ is not equal to $0$ for every $x$ belongs to $[0,2)$.

My process is shown in the image in the attachment.
Please suggest what can I further do to get the result. Also suggest if you have any other method for the question.

algebra-precalculus

share|cite|improve this question

edited Aug 3 at 6:20

user529760

509216

asked Jul 31 at 18:18

jayant98

94

put on hold as off-topic by amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco Aug 5 at 7:10

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I don't think the title is appropriate. Functional analysis is something different.
  – Rumpelstiltskin
  Jul 31 at 18:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Then what it should be?
  – jayant98
  Jul 31 at 18:22
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Functional equations. Other than that, questions should ask one thing at a time.
  – Rumpelstiltskin
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is the topic of so-called "functional equations", I would change the title to reflect that.
  – Nico
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @jayant98 Why did you roll back my MathJax edit?
  – packetpacket
  Aug 1 at 19:36
  
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

1

up vote
-1
down vote

favorite

1

1

Question
Find all (if any) functions $f$ taking the non-negative reals onto the
non-negative reals, such that

(a) $f(x(f(y))cdot f(y)= f(x + y)$ for all non-negative $x, y$;

(b) $f(2)=0$;

(c) $f(x)$ is not equal to $0$ for every $x$ belongs to $[0,2)$.

My process is shown in the image in the attachment.
Please suggest what can I further do to get the result. Also suggest if you have any other method for the question.

algebra-precalculus

share|cite|improve this question

edited Aug 3 at 6:20

user529760

509216

asked Jul 31 at 18:18

jayant98

94

Question
Find all (if any) functions $f$ taking the non-negative reals onto the
non-negative reals, such that

(a) $f(x(f(y))cdot f(y)= f(x + y)$ for all non-negative $x, y$;

(b) $f(2)=0$;

(c) $f(x)$ is not equal to $0$ for every $x$ belongs to $[0,2)$.

My process is shown in the image in the attachment.
Please suggest what can I further do to get the result. Also suggest if you have any other method for the question.

algebra-precalculus

share|cite|improve this question

edited Aug 3 at 6:20

user529760

509216

asked Jul 31 at 18:18

jayant98

94

share|cite|improve this question

share|cite|improve this question

edited Aug 3 at 6:20

user529760

509216

edited Aug 3 at 6:20

user529760

509216

edited Aug 3 at 6:20

user529760

509216

509216

asked Jul 31 at 18:18

jayant98

94

asked Jul 31 at 18:18

jayant98

94

asked Jul 31 at 18:18

jayant98

94

94

put on hold as off-topic by amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco Aug 5 at 7:10

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco Aug 5 at 7:10

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Tyrone, Xander Henderson, Leucippus, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I don't think the title is appropriate. Functional analysis is something different.
  – Rumpelstiltskin
  Jul 31 at 18:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Then what it should be?
  – jayant98
  Jul 31 at 18:22
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Functional equations. Other than that, questions should ask one thing at a time.
  – Rumpelstiltskin
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is the topic of so-called "functional equations", I would change the title to reflect that.
  – Nico
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @jayant98 Why did you roll back my MathJax edit?
  – packetpacket
  Aug 1 at 19:36
  
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I don't think the title is appropriate. Functional analysis is something different.
  – Rumpelstiltskin
  Jul 31 at 18:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Then what it should be?
  – jayant98
  Jul 31 at 18:22
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Functional equations. Other than that, questions should ask one thing at a time.
  – Rumpelstiltskin
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is the topic of so-called "functional equations", I would change the title to reflect that.
  – Nico
  Jul 31 at 18:23
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @jayant98 Why did you roll back my MathJax edit?
  – packetpacket
  Aug 1 at 19:36
  
  

  
  
  
  

1

1

I don't think the title is appropriate. Functional analysis is something different.
– Rumpelstiltskin
Jul 31 at 18:21

I don't think the title is appropriate. Functional analysis is something different.
– Rumpelstiltskin
Jul 31 at 18:21

Then what it should be?
– jayant98
Jul 31 at 18:22

Then what it should be?
– jayant98
Jul 31 at 18:22

1

1

Functional equations. Other than that, questions should ask one thing at a time.
– Rumpelstiltskin
Jul 31 at 18:23

Functional equations. Other than that, questions should ask one thing at a time.
– Rumpelstiltskin
Jul 31 at 18:23

This is the topic of so-called "functional equations", I would change the title to reflect that.
– Nico
Jul 31 at 18:23

This is the topic of so-called "functional equations", I would change the title to reflect that.
– Nico
Jul 31 at 18:23

1

1

@jayant98 Why did you roll back my MathJax edit?
– packetpacket
Aug 1 at 19:36

@jayant98 Why did you roll back my MathJax edit?
– packetpacket
Aug 1 at 19:36

 | 
show 1 more comment

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