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Challenge: If f(3x + 2) = 9x² + 12x - 1, then f(k - 1) =

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by Brent@GMATPrepNow » Sun Aug 12, 2018 6:32 am

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E

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Difficulty—

If f(3x + 2) = 9x² + 12x - 1, then f(k - 1) =

A) k² - 2k - 6
B) k² - 2k - 5
C) k² - 2k - 4
D) k² - 2k + 1
E) k² - 2k + 5

Answer: C
Difficulty level: 700+
Source: www.gmatprepnow.com

* I'll post a solution in 2 days
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by regor60 » Mon Aug 13, 2018 7:27 am
Brent@GMATPrepNow wrote:If f(3x + 2) = 9x² + 12x - 1, then f(k - 1) =

A) k² - 2k - 6
B) k² - 2k - 5
C) k² - 2k - 4
D) k² - 2k + 1
E) k² - 2k + 5

Answer: C
Difficulty level: 700+
Source: www.gmatprepnow.com

* I'll post a solution in 2 days
What operation can be done to (3X+2) to make it equal to 9X^2 +12X-1 ?

It sure looks pretty close to the square of (3X+2) = (3X+2)(3X+2) = 9X^2 + 12X + 4, except it is lower by 5

So an operation that fits is to square it and subtract 5. So let's apply to (k-1),

(K-1)(K-1)= K^2 - 2K + 1. Subtract 5 = [spoiler]K^2-2K-4 , C[/spoiler]
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by Brent@GMATPrepNow » Tue Aug 14, 2018 5:22 am
Brent@GMATPrepNow wrote:If f(3x + 2) = 9x² + 12x - 1, then f(k - 1) =

A) k² - 2k - 6
B) k² - 2k - 5
C) k² - 2k - 4
D) k² - 2k + 1
E) k² - 2k + 5
Given: f(3x + 2) = 9x² + 12x - 1

First notice that 9x² + 12x - 1 looks a lot like how (3x + 2)² looks when we expand an simplify it.
Notice that (3x + 2)² = 9x² + 12x + 4
This is VERY similar to 9x² + 12x - 1
In fact, if we take 9x² + 12x + 4 and subtract 5, we get 9x² + 12x - 1
That is: 9x² + 12x + 4 - 5 = 9x² + 12x - 1

So, we can write: f(3x + 2) = 9x² + 12x - 1
= 9x² + 12x + 4 - 5
= (3x + 2)² - 5

In other words, f(something) = (something)² - 5
So, for example, f(y) = y² - 5
And f(7) = 7² - 5

Likewise, f(k - 1) = (k - 1)² - 5
= k² - 2k + 1 - 5
= k² - 2k - 4

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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