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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If f(2x - 1) = 4x² - 4x - 8, then f(5) =
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12 Aug 2018, 05:53
12 Aug 2018, 05:53
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If f(2x - 1) = 4x² - 4x - 8, then f(5) =
A) 16
B) 18
C) 36
D) 48
E) 72
A) 16
B) 18
C) 36
D) 48
E) 72
Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) =
[#permalink]
12 Aug 2018, 06:07
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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) =
[#permalink]
01 Jun 2020, 11:07
01 Jun 2020, 11:07
GreenlightTestPrep wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =
A) 16
B) 18
C) 36
D) 48
E) 72
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
