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If f(2x - 1) = 4x² - 4x - 8, then f(5) =

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If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink] New post 12 Aug 2018, 05:53
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80% (00:47) correct 20% (01:40) wrong based on 35 sessions
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72
[Reveal] Spoiler: OA

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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink] New post 12 Aug 2018, 06:07
GreenlightTestPrep wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72



Here,

\(2x - 1 = 5\)

or\(2x = 6\)

or \(x = 3\)

Now \(f(5) = 4 * 3^2 - 4 * 3 - 8 = 36 - 12 - 8 = 36 - 20 = 16\)

Hence option A
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GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 3827
Followers: 148

Kudos [?]: 4472 [0], given: 69

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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink] New post 01 Jun 2020, 11:07
Expert's post
GreenlightTestPrep wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72


First notice that 4x² - 4x - 8 looks a lot like (2x - 1)²

(2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1

Now take: f(2x - 1) = 4x² - 4x - 8
Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9
In other words, f(something) = something² - 9

In general, we can write f(x) = x² - 9

We're asked to evaluate f(5)
So f(5) = 5² - 9 = 25 - 9 = 16

Answer: A

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) =   [#permalink] 01 Jun 2020, 11:07
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