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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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petercao
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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] New post   Updated on: 07 Mar 2017, 01:19
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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)
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A

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.
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fluke
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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] 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 [#permalink] New post   13 Aug 2017, 19:26
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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 for all x, then f(1 [#permalink] New post   14 Aug 2017, 00:46
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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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Re: If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1 [#permalink] 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] 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] 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] 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 [#permalink] 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 [#permalink]
13 Aug 2017, 19:45
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