 It is currently 24 May 2019, 15:44 ### 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. # f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1860 , given: 397

f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]
Expert's post 00:00

Question Stats: 66% (01:08) correct 33% (00:00) wrong based on 15 sessions
$$f(x) = 3x^2$$
$$g(x) = x + 1$$
x is an integer such that –10 ≤ x ≤ –1.

 Quantity A Quantity B f(g(x)) g(f(x))

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 2
Question: 11
Page: 551
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Manager Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 109  , given: 22

Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]
1
This post received
KUDOS
Answer: A
f (x) = 3 * x^2
g(x) = x + 1
A: f(g(x)) = f(x + 1) = 3 * (x + 1)^2 = 3x^2 + 6x + 3
B: g(f(x) = g (3 * x^2) = 3 * x^2 + 1
So we should compare 6x+3 with 1.
-10 <= x <= -1 so -57 <= 6x+3 <= -3
As 6x+3 is always less than 1, B is bigger than A.

_________________

Follow your heart

GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1860 , given: 397

Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]
Expert's post
Explanation

Plugging 10 values into two compound functions is going to involve lots of arithmetic and will take a long time, so it is better to do this one algebraically.

Working from the inside out, find Quantity A: $$f(g(x))=f(x+1)=3(x+1)^2=3x^2+6x+3$$; remember to FOIL the (x + 1) when you square it. Similarly, find Quantity B: $$g(f(x)) = g(3x^2) = 3x^2 + 1$$.

You can add or subtract the same value from both quantities without affecting which is bigger; doing so with $$3x^2 + 1$$ leaves you with 6x + 2 in Quantity A and 0 in Quantity B.

Because 6x + 2 is a linear function whose graph is a line with positive slope, you know that the values of the function will increase as the values of x increase.

So you only need to plug in the endpoints of the given range of x-values to see what happens to the function: 6(–10) + 2 = –58 and 6(–1) + 2 = –4.

So all possible values of Quantity A are still less than 0, and the answer is choice (B).
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤   [#permalink] 06 Apr 2018, 15:10
Display posts from previous: Sort by

# f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.