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

Expert replies

Previous Topic Next Topic

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; 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

Timer

00:00

Your answer

Difficulty–

right wrong

Pick an answer to see how members did

If f(2x - 1) = 4x² - 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

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.

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) = 4x² - 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

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; 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) = 4x² - 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 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

Brent Hanneson - Creator of GMATPrepNow.com

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review