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f(x) = x2 + 1 g(x) = x – 2

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f(x) = x2 + 1 g(x) = x – 2 [#permalink] New post 24 Mar 2018, 02:35
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Question Stats:

86% (00:16) correct 13% (00:19) wrong based on 15 sessions
\(f(x) = x^2 + 1\)
\(g(x) = x - 2\)

Quantity A
Quantity B
f(g(–1))
g(f(–1))


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 1
Question: 11
Page: 548
[Reveal] Spoiler: OA

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Re: f(x) = x2 + 1 g(x) = x – 2 [#permalink] New post 26 Mar 2018, 18:49
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This is a function problem involving nested functions. An easy way of thinking of functions is as though they're a find and replace in a word processing document. For example, if f(x) = x^2 + 2x + 1, then when they give you f(2), you can simply replace every x you see with a 2, giving you 2^2 + 2x2 + 1 = 9.

In quantity A and B they've given us nested functions, one inside the other. In cases like these, simply do the inside one first, then the outside one next. Since quantity A is f(g(–1)), let's do g(-1) first. Since g(x) = x - 2, we can substitute x for -1, giving us -1 - 2 = -3. Now we plug -3 into the outside function, which is f(x) = x^2 + 1, giving us (-3)^2 + 1 = 10.

Let's do the same for quantity B, in which the inside function is f(x). So we'll plug -1 into f(x) first, and then the result into g(x) next. Plugging -1 into x^2 + 1 gives us (-1)^2 + 1 = 2, and plugging 2 into x - 2 gives us 2 - 2 = 0.

Since quantity A gives us 10 and quantity B gives us 0, the answer is A.
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4722
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1630 [0], given: 390

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Re: f(x) = x2 + 1 g(x) = x – 2 [#permalink] New post 04 Apr 2018, 15:49
Expert's post
Explanation

For Quantity A, start with the innermost parentheses: \(g(-1) = (-1) - 2 = -3\).

So \(f(-3) = (-3)^2 + 1 = 9 + 1 = 10\).

For Quantity B, \(f(-1) = (-1)^2 + 1 = 1 + 1 = 2\). So, \(g(2) = 2 - 2 = 0\).

Thus, Quantity A is greater.
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Re: f(x) = x2 + 1 g(x) = x – 2   [#permalink] 04 Apr 2018, 15:49
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