Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 24 May 2017, 05:50

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 01 Jul 2012
Posts: 84
Location: United States
GMAT 1: 510 Q34 V28
GMAT 2: 580 Q35 V35
GMAT 3: 640 Q34 V44
GMAT 4: 690 Q43 V42
GPA: 3.61
WE: Education (Education)
Followers: 13

Kudos [?]: 130 [0], given: 16

If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink]

Show Tags

New post 10 Jul 2013, 12:52
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:44) correct 0% (00:00) wrong based on 24 sessions

HideShow timer Statistics

If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does f(g(x)) = g(f(x))?


f(2x)=g(x^3+1)

I'm stuck at this point. Please help!

Last edited by Bunuel on 10 Jul 2013, 13:02, edited 1 time in total.
Edited the question.
Expert Post
1 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38853
Followers: 7723

Kudos [?]: 105977 [1] , given: 11602

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink]

Show Tags

New post 10 Jul 2013, 13:10
1
This post received
KUDOS
Expert's post
josemnz83 wrote:
If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does f(g(x)) = g(f(x))?


f(2x)=g(x^3+1)

I'm stuck at this point. Please help!


Given: \(f(x) = x^3 + 1\) and \(g(x) = 2x\).

LHS: \(f(g(x))=f(2x)=(2x)^3+1=8x^3+1\)

RHS: \(g(f(x))=g(x^3+1)=2(x^3+1)=2x^3+2\)

So, we have that \(8x^3+1=2x^3+2\) --> \(x^3=\frac{1}{6}\) --> \(x=\frac{1}{\sqrt[3]{6}}\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 01 Jul 2012
Posts: 84
Location: United States
GMAT 1: 510 Q34 V28
GMAT 2: 580 Q35 V35
GMAT 3: 640 Q34 V44
GMAT 4: 690 Q43 V42
GPA: 3.61
WE: Education (Education)
Followers: 13

Kudos [?]: 130 [0], given: 16

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink]

Show Tags

New post 10 Jul 2013, 13:18
On the RHS, g(x)=2x. You wrote 2(x^3+1). What happened to the x in the 2x? That is where I get lost.
Thanks!
Bunuel wrote:
josemnz83 wrote:
If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does f(g(x)) = g(f(x))?

f(2x)=g(x^3+1)

I'm stuck at this point. Please help!


Given: \(f(x) = x^3 + 1\) and \(g(x) = 2x\).

LHS: \(f(g(x))=f(2x)=(2x)^3+1=8x^3+1\)

RHS: \(g(f(x))=g(x^3+1)=2(x^3+1)=2x^3+2\)

So, we have that \(8x^3+1=2x^3+2\) --> \(x^3=\frac{1}{6}\) --> \(x=\frac{1}{\sqrt[3]{6}}\).

Hope it's clear.
Expert Post
1 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38853
Followers: 7723

Kudos [?]: 105977 [1] , given: 11602

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink]

Show Tags

New post 10 Jul 2013, 13:23
1
This post received
KUDOS
Expert's post
josemnz83 wrote:
On the RHS, g(x)=2x. You wrote 2(x^3+1). What happened to the x in the 2x? That is where I get lost.
Thanks!
Bunuel wrote:
josemnz83 wrote:
If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does f(g(x)) = g(f(x))?

f(2x)=g(x^3+1)

I'm stuck at this point. Please help!


Given: \(f(x) = x^3 + 1\) and \(g(x) = 2x\).

LHS: \(f(g(x))=f(2x)=(2x)^3+1=8x^3+1\)

RHS: \(g(f(x))=g(x^3+1)=2(x^3+1)=2x^3+2\)

So, we have that \(8x^3+1=2x^3+2\) --> \(x^3=\frac{1}{6}\) --> \(x=\frac{1}{\sqrt[3]{6}}\).

Hope it's clear.


This might help: \(g(n) = 2n\) --> \(g(x^3+1)=2(x^3+1)\) (\(n=x^3+1\)).
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15418
Followers: 649

Kudos [?]: 206 [0], given: 0

Premium Member
Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink]

Show Tags

New post 02 May 2017, 23:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does   [#permalink] 02 May 2017, 23:33
    Similar topics Author Replies Last post
Similar
Topics:
2 What is the value of x: |x+2|+|x-3| = |2x+3|? nguyendinhtuong 3 08 Jan 2017, 15:09
2 Experts publish their posts in the topic If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the zxcvbnmas 2 04 Feb 2016, 21:14
7 Experts publish their posts in the topic Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6) Bunuel 7 03 Mar 2017, 23:32
34 Experts publish their posts in the topic If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum Bunuel 16 10 Apr 2017, 03:18
If g(x) = 3x + x^(1/2), what is the value of g(d^2 +6d+9)? nelvin898 1 09 Feb 2011, 02:31
Display posts from previous: Sort by

If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.