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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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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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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)
[Reveal] Spoiler: OA

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.

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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]

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New post 15 Nov 2008, 14:11
Just substitute (1-x) for x and you will see that f(1-x) is nothing but f(x)

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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]

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New post 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)

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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]

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New post 03 Sep 2011, 09:35
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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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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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New post 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!!

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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]

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New post 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)

Answer is A.

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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]

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If f is the function defined by f(x) = x^2 (1-x)^2 [#permalink]

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New post 13 Aug 2017, 19:10
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)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you

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Re: If f is the function defined by f(x) = x^2 (1-x)^2 [#permalink]

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New post 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)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


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

Answer A
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Re: If f is the function defined by f(x) = x^2 (1-x)^2 [#permalink]

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New post 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)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


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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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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New post 14 Aug 2017, 00:41
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)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


Merging topics. Please refer to the discussion above.
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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]

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New post 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)

Can someone please help me with the method of substituting the numbers and finding out the answer for this question. Thank you


13. Functions



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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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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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