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If f(2x - 1) = 4xÂ² - 4x - 8, then f(5) =

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 12, 2018 5:44 am

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If f(2x - 1) = 4xÂ² - 4x - 8, then f(5) =

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

Answer: A
Difficulty level: 600 (ish)
Source: www.gmatprepnow.com

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Sun Aug 12, 2018 5:44 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Sep 01, 2018 2:19 pm

$$Let\ 2x\ -1\ =\ y\ and\ x\ =\ \frac{\left(y\ +\ 1\right)}{2}$$
$$f\left(y\right)=4\ \left(\frac{\left(y\ +\ 1\right)}{2}\right)^2-\ 4\ \left(\frac{y\ +\ 1}{2}\right)-\ 8$$
$$f\left(y\right)=\left(y\ +\ 1\right)^2-\ 2\ \left(y\ +\ 1\right)-\ 8$$
$$f\left(y\right)=y^2+1\ \left(-2y\ -\ 2y\right)?\left(-2-\ 8\right)$$
$$f\left(y\right)=y^2\ -\ 9$$
If y = 5
$$f\left(5\right)=5^2\ -\ 9$$
f (5) = 25 - 9
f(5) = 16.

Option A is CORRECT.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Sep 02, 2018 11:07 am

Brent@GMATPrepNow wrote:If f(2x - 1) = 4xÂ² - 4x - 8, then f(5) =

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

\[f\left( {2x - 1} \right) = 4{x^2} - 4x - 8\]
\[? = f\left( 5 \right)\]
\[{\text{Take}}\,\,x = 3\,\,\,\,\left( {{\text{so}}\,\,{\text{that}}\,\,\,2x - 1 = 5} \right)\]
\[? = f\left( {2 \cdot \boxed3 - 1} \right) = 4 \cdot {\boxed3^2} - 4 \cdot \boxed3 - 8 = 16\,\,\,\,\]

The above follows the notations and rationale taught in the GMATH method.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Apr 18, 2019 7:33 am

Brent@GMATPrepNow wrote:If f(2x - 1) = 4xÂ² - 4x - 8, then f(5) =

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

Answer: A
Difficulty level: 600 (ish)
Source: www.gmatprepnow.com

Here's one more approach:

First notice that 4xÂ² - 4x - 8 looks a lot like (2x - 1)Â²

(2x - 1)Â² = (2x - 1)(2x - 1) = 4xÂ² - 4x + 1

Now take: f(2x - 1) = 4xÂ² - 4x - 8
Rewrite as: f(2x - 1) = 4xÂ² - 4x + 1 - 9 = (2x - 1)Â² - 9
In other words, f(something) =somethingÂ² - 9

In general, we can write f(x) = xÂ² - 9

We're asked to evaluate f(5)
So f(5) = 5Â² - 9 = 25 - 9 = 16

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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