GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Apr 2019, 21:18

### 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

# If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Nov 2008
Posts: 27
If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

Updated on: 07 Mar 2017, 01:19
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:21) correct 24% (02:15) wrong based on 163 sessions

### HideShow timer Statistics

If f is the function defined by $$f(x) = x^2*(1-x)^2$$ for all x, then f(1-x) =

A. f(x)
B. f(x)^2
C. 1 - f(x)
D. (1-x)*f(x)
E. f(1) - f(x)

Originally posted by petercao on 14 Nov 2008, 16:41.
Last edited by Bunuel on 07 Mar 2017, 01:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
VP
Joined: 05 Jul 2008
Posts: 1220
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

15 Nov 2008, 14:11
Just substitute (1-x) for x and you will see that f(1-x) is nothing but f(x)
Senior Manager
Joined: 30 Aug 2009
Posts: 266
Location: India
Concentration: General Management
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

03 Sep 2011, 09:24
DeeptiM wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

replace x by 1-x in the original expression and we would get f(1-x) = f(x)
Retired Moderator
Joined: 20 Dec 2010
Posts: 1784
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

03 Sep 2011, 09:35
1
2
petercao wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =

A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

$$f(x) = x^2 (1-x)^2$$

What is $$f(1-x)$$?

Just replace x with (1-x)
$$f(1-x) = (1-x)^2 (1-(1-x))^2$$
$$f(1-x) = (1-x)^2 (x)^2$$
$$f(1-x) = (x)^2(1-x)^2 = f(x)$$

Ans: "A"
********************************

Or pick x=3; 1-x=1-3=-2
$$f(1-x)=f(-2)=(-2)^2*(1-(-2))^2=4*9=36$$

Let's check each option separately:

A. f(x)
$$f(3)=3^2*(1-3)^2=9*4=36$$. Holds good. Possible answer.

B. [f(x)]^2
$$(36)^2$$. Ignore

C. 1 - f(x)
$$1-36=-35$$. Ignore

D. (1-x) f(x)
$$(1-3)(36)=36*-2=-72$$. Ignore

E. f(1) - f(x)
$$1^2*(1-1)^2-36=0-36=-36$$. Ignore.

Only A gave us what we got with f(1-x) i.e. f(-2).

Ans: "A"
_________________
Manager
Joined: 16 Feb 2011
Posts: 198
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

03 Sep 2011, 09:43
Thanks a lot fluke...i did the first way by replacing x with 1-x but then....god knows from where did i start converting the equation in (a+b)^2 form...silly me...

thanks again!!
Director
Joined: 01 Feb 2011
Posts: 646
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

03 Sep 2011, 10:05
f(x) = x^2 * (1-x)^2

substituting x with 1-x , we should get f(1-x)

f(1-x) = (1-x)^2 * (1-(1-x))^2
= (1-x)^2 *x^2
= f(x)

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1354
Location: Viet Nam
Re: If f is the function defined by f(x) = x^2 (1-x)^2  [#permalink]

### Show Tags

13 Aug 2017, 19:26
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

$$f(x)=x^2(1-x)^2 \implies f(1-x)=(1-x)^2(1-(1-x))^2=(1-x)^2x^2=f(x)$$

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: If f is the function defined by f(x) = x^2 (1-x)^2  [#permalink]

### Show Tags

13 Aug 2017, 19:45
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

Hi longhaul123,

Please find the method of number substitution

If x=2, f(x) = 4(1) = 4
So, f(1-x) = f(-1) = $$1(1 -(-1))^2 = 1(4) = 4$$ = f(x) (Option A)

Hope that helps!
_________________
You've got what it takes, but it will take everything you've got
Math Expert
Joined: 02 Sep 2009
Posts: 54496
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1  [#permalink]

### Show Tags

14 Aug 2017, 00:46
longhaul123 wrote:
If f is the function defined by f(x) = x^2 (1-x)^2 for all x, then f(1-x) =
A. f(x)
B. [f(x)]^2
C. 1 - f(x)
D. (1-x) f(x)
E. f(1) - f(x)

13. Functions

_________________
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1   [#permalink] 14 Aug 2017, 00:46
Display posts from previous: Sort by