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

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If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink] New post 10 Jul 2013, 11:52
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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, 12:02, edited 1 time in total.
Edited the question.
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Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink] New post 10 Jul 2013, 12:10
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.
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Current Student
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Joined: 30 Jun 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: 8

Kudos [?]: 88 [0], given: 16

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink] New post 10 Jul 2013, 12:18
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
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Joined: 02 Sep 2009
Posts: 23422
Followers: 3617

Kudos [?]: 28975 [1] , given: 2874

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does [#permalink] New post 10 Jul 2013, 12:23
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does   [#permalink] 10 Jul 2013, 12:23
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