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# f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1731 [0], given: 397

f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]  26 Mar 2018, 15:57
Expert's post
00:00

Question Stats:

58% (00:45) correct 41% (00:00) wrong based on 12 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

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Manager
Joined: 22 Feb 2018
Posts: 156
Followers: 2

Kudos [?]: 94 [1] , given: 21

Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]  26 Mar 2018, 17:50
1
KUDOS
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.

_________________

GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1731 [0], given: 397

Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤ [#permalink]  06 Apr 2018, 15:10
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).
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Re: f(x) = 3x2 g(x) = x + 1 x is an integer such that –10 ≤ x ≤   [#permalink] 06 Apr 2018, 15:10
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