 It is currently 19 Sep 2020, 07:51 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Argument of Composition  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern Joined: 22 Aug 2018
Posts: 29
Followers: 0

Kudos [?]: 6 , given: 4 00:00

Question Stats: 78% (01:48) correct 21% (01:32) wrong based on 19 sessions
The functions $$f(x)$$ and $$g(x)$$ are defined by $$f(x) = x^2 – 1$$ and $$g(x) = 1 – 2x$$. Given that $$f(g(k)) = 3$$, which of the following could be the value of k?

Options
A. $$\frac{1}{2}$$

B. $$\frac{√3}{2}$$

C. $$1$$

D. $$\frac{3}{2}$$

E.$$-1$$
[Reveal] Spoiler: OA

Last edited by rajlal on 15 Sep 2018, 02:40, edited 1 time in total.
Intern Joined: 21 Aug 2018
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 0

goof VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1308  , given: 251

1
KUDOS
rajlal wrote:
The functions $$f(x)$$ and $$g(x)$$ are defined by $$f(x) = x^2 – 1$$ and $$g(x) = 1 – 2x$$. Given that $$f(g(k)) = 3$$, which of the following could be the value of k?

Options
A. $$\frac{1}{2}$$

B. $$\frac{√3}{2}$$

C. $$1$$

D. $$\frac{3}{2}$$

E.$$-1$$

Why does the method of substitution give me the wrong answer?

Given $$f(x) = x^2 - 1$$ and $$g(x)= 1 - 2x$$

Now
$$g(k) = 1 - 2k$$
$$f(g(k)) = (1 - 2k)^2 - 1$$

But $$f(g(k)) = 3$$

so,
$$3 = (1 - 2k)^2 - 1$$

or $$4k^2 - 4k - 3 = 0$$

or $$4k^2 -6k + 2k - 3 = 0$$

or $$k^2 - \frac{3k}{2} +\frac{k}{2} - \frac{3}{4} = 0$$

or $$(k - \frac{3}{2})(k +\frac{1}{2}) = 0$$

we get $$k = -\frac{1}{2} or \frac{3}{2}$$

Only Option D is correct
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests Re: Argument of Composition   [#permalink] 15 Sep 2018, 06:01
Display posts from previous: Sort by

# Argument of Composition  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.