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

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Intern
Joined: 08 Nov 2008
Posts: 29
If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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Updated on: 07 Mar 2017, 01:19
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25% (medium)

Question Stats:

66% (01:15) correct 34% (01:54) wrong based on 138 sessions

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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: 1340
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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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: 276
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]

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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)
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1901
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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03 Sep 2011, 09:35
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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"
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Joined: 16 Feb 2011
Posts: 227
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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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: 686
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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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!
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Posts: 1387
Location: Viet Nam
Re: If f is the function defined by f(x) = x^2 (1-x)^2 [#permalink]

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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)

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

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Joined: 26 Feb 2016
Posts: 2797
Location: India
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Re: If f is the function defined by f(x) = x^2 (1-x)^2 [#permalink]

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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!
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Math Expert
Joined: 02 Sep 2009
Posts: 46062
Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink]

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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

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

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