 It is currently 22 Jul 2019, 19:37 ### 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. # f(x) = x2 + 1. For which values of x does f(x) =  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 7426
Followers: 126

Kudos [?]: 1457 , given: 6628

f(x) = x2 + 1. For which values of x does f(x) = [#permalink]
Expert's post 00:00

Question Stats: 72% (00:46) correct 27% (01:04) wrong based on 36 sessions

$$f(x) = x^2 + 1$$. For which values of x does $$f(x) = f (\frac{1}{x})$$?

Indicate all such values:

❑ $$-2$$

❑ $$-1$$

❑ $$-\frac{1}{2}$$

❑ $$\frac{1}{2}$$

❑ 1

❑ 2
[Reveal] Spoiler: OA

_________________
Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 363 , given: 66

Re: f(x) = x2 + 1. For which values of x does f(x) = [#permalink]
It is quite straightforward to notice that the only value of x that are equal when considered as 1/x are -1 and +1. Since in the formula for f(x) the x is squared and then summed to 1, it is easy to see that every other solution would have lead to two different values when considering x and 1/x. Director Joined: 20 Apr 2016
Posts: 948
WE: Engineering (Energy and Utilities)
Followers: 13

Kudos [?]: 709  , given: 152

Re: f(x) = x2 + 1. For which values of x does f(x) = [#permalink]
1
KUDOS
Carcass wrote:

$$f(x) = x^2 + 1$$. For which values of x does $$f(x) = f (\frac{1}{x})$$?

Indicate all such values:

❑ -2

❑ -1

❑ $$\frac{-1}{2}$$

❑ 1/2

❑ 1

❑ 2

[Reveal] Spoiler: OA
B and E

We have $$f(x) = f (\frac{1}{x})$$ and given f(x) =$$x^2$$+1

now substituting we get -

$$x^2$$+1 = $$(\frac{1}{x})^2$$ +1

or $$x^2$$+1 = $$\frac{1+x^2}{x^2}$$

or cross multiflication

$$x^4$$+$$x^2$$ = 1+ $$x^2$$

or $$x^4$$ =1

Only -1 and 1 fits the equation
_________________

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

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html Re: f(x) = x2 + 1. For which values of x does f(x) =   [#permalink] 24 Sep 2017, 12:11
Display posts from previous: Sort by

# f(x) = x2 + 1. For which values of x does f(x) =  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®.