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Big theta and function composition [closed]

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-1

$begingroup$

This is an assignment for a Discrete Math class. We are asked to show that this is true. However, I believe it is false.

If $f_1$ and $f_2$ are functions from the set of positive integers to the set of real numbers and $f_1$ is $Theta(g_1)$ and $f_2$ is $Theta(g_2)$, then $(f_1 circ f_2)$ is $Theta(g_1 circ g_2)$.

Could you help me with it?

discrete-mathematics

share|cite|improve this question

edited Mar 13 at 3:25

Mehrdad Mirzaei

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

$endgroup$

closed as off-topic by Eevee Trainer, RRL, Lee David Chung Lin, Shailesh, Leucippus Mar 13 at 1:36

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." – Eevee Trainer, RRL, Lee David Chung Lin, Shailesh, Leucippus

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

add a comment | 

-1

$begingroup$

This is an assignment for a Discrete Math class. We are asked to show that this is true. However, I believe it is false.

If $f_1$ and $f_2$ are functions from the set of positive integers to the set of real numbers and $f_1$ is $Theta(g_1)$ and $f_2$ is $Theta(g_2)$, then $(f_1 circ f_2)$ is $Theta(g_1 circ g_2)$.

Could you help me with it?

discrete-mathematics

share|cite|improve this question

edited Mar 13 at 3:25

Mehrdad Mirzaei

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

$endgroup$

closed as off-topic by Eevee Trainer, RRL, Lee David Chung Lin, Shailesh, Leucippus Mar 13 at 1:36

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." – Eevee Trainer, RRL, Lee David Chung Lin, Shailesh, Leucippus

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

add a comment | 

$begingroup$

This is an assignment for a Discrete Math class. We are asked to show that this is true. However, I believe it is false.

If $f_1$ and $f_2$ are functions from the set of positive integers to the set of real numbers and $f_1$ is $Theta(g_1)$ and $f_2$ is $Theta(g_2)$, then $(f_1 circ f_2)$ is $Theta(g_1 circ g_2)$.

Could you help me with it?

discrete-mathematics

share|cite|improve this question

edited Mar 13 at 3:25

Mehrdad Mirzaei

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

$endgroup$

share|cite|improve this question

edited Mar 13 at 3:25

Mehrdad Mirzaei

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

share|cite|improve this question

edited Mar 13 at 3:25

Mehrdad Mirzaei

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

asked Mar 12 at 22:08

Mehrdad MirzaeiMehrdad Mirzaei

14

1 Answer
1

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oldest

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0

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I guess, $f_1(x)=g_1(x)=e^x$, $f_2(x)=x^2$, $g_2(x)=x^2+x$, but of course $e^{x^2}notin Theta( e^{x^2+x})$ since $e^{x^2}in o(e^{x^2+x})$.

share|cite|improve this answer

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

$endgroup$

add a comment | 

0

$begingroup$

I guess, $f_1(x)=g_1(x)=e^x$, $f_2(x)=x^2$, $g_2(x)=x^2+x$, but of course $e^{x^2}notin Theta( e^{x^2+x})$ since $e^{x^2}in o(e^{x^2+x})$.

share|cite|improve this answer

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

$endgroup$

add a comment | 

0

$begingroup$

I guess, $f_1(x)=g_1(x)=e^x$, $f_2(x)=x^2$, $g_2(x)=x^2+x$, but of course $e^{x^2}notin Theta( e^{x^2+x})$ since $e^{x^2}in o(e^{x^2+x})$.

share|cite|improve this answer

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

$endgroup$

add a comment | 

$begingroup$

I guess, $f_1(x)=g_1(x)=e^x$, $f_2(x)=x^2$, $g_2(x)=x^2+x$, but of course $e^{x^2}notin Theta( e^{x^2+x})$ since $e^{x^2}in o(e^{x^2+x})$.

share|cite|improve this answer

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

$endgroup$

share|cite|improve this answer

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627

answered Mar 12 at 22:15

Saucy O'PathSaucy O'Path

6,1391627