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

Question

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

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

BrentGMATPrepNow · Accepted Answer

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

PKN · Answer

Given,  f(3x + 2)  =  9x^2 + 12x - 1 =  9x² + 12x +4 -4-1=(3x+2)^2 - 5 
Or,  f(k) = k^2 - 5  , where k=3x+2

So,  f(k-1)=(k-1)^2-5=k^2-2k+1-5=k^2-2k-4

Ans. (C)

HKD1710 · Answer

3x+2 = k-1
3x = k-3

Put the value of 3x in 9x^2 + 12x - 1

f(k-1)=f(3x+2)= 9x^2 + 12x - 1 
f(k-1)=f(3x+2)= 3x*3x + 4*3x -1 now put 3x = k-3
f(k-1)=f(3x+2)= (k-3)(k-3) + 4(k-3) -1
f(k-1)=f(3x+2)= k^2 - 2k - 4

souvonik2k · Answer

f(3x + 2) = 9x^2 + 12x - 1 
We see that  (3x+2)^2  =  9x^2 + 12x + 4  , if we subtract 5 from this, we get the desired value.
So, f(3x + 2) =  (3x+2)^2 - 5  =  9x^2 + 12x - 1 
f(k-1) =  (k-1)^2-5  =  k^2 - 2k +1 - 5  =  k^2- 2k - 4  
Answer C.

manjot123 · Answer

3x+2 = k-1 x= k-3/3
9(k-3/3)^2 +12(k-3/3) -1
K^2 + 9 -6k +4k -12 -1
K^2 -2k -4

Posted from my mobile device

Loser94 · Answer

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)^2 = 9x^2+12x−1
(3x+2)^2 =9x^2+12x+4
F(x)=x^2-5
So f(k-1)=k² - 2k - 4

B option

Posted from my mobile device

GMATGuruNY · Answer

Alternate approach:

Let k=1, with the result that f(k-1) = f(0).
The question stem becomes:
If f(3x + 2) =  9x² + 12x - 1 , what is the value of f(0)?

Since f(3x+2) = f(0) when x=-2/3, plug x=-2/3 into the expression in blue:
 9(-\frac{2}{3})^2 + 12(-\frac{2}{3}) - 1 = 4 - 8 - 1 = -5

Now plug k=1 into the answer choices to see which yields the target value of -5.
Only C works:
 k^2 - 2k - 4 = 1 - 2 - 4 = -5

C

Bismarck · Answer

OA:C 
Let  3x+2 = y

3x =y-2

x= \frac{y-2}{3}

f(3x + 2) = 9x² + 12x - 1

f(y) = 9 (\frac{y-2}{3})^2 +12(\frac{y-2}{3}) -1

f(y) = (y-2)^2 +4(y-2) -1=y^2+4-2*2y + 4y -8 -1 =y^2-5

f(y)=y^2-5

f(k - 1) =(k-1)^2-5 =k^2+1-2k-5 =k^2-2k-4

Mo2men · Answer

Dear Brent,

Very enlightening answer. Your way above answered my question in simple terms.

Thanks

dhruva09 · Answer

Bunuel , Kindly correct the format for 9X2 as 9x^2 and k2 as k^2 in the choices.

Bunuel · Answer

Done. Thank you for noticing and notifying.

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

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