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For which of the following functions f is f(x) = f(1-x) for

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For which of the following functions f is f(x) = f(1-x) for [#permalink] New post 18 Aug 2008, 12:58
For which of the following functions f is f(x) = f(1-x) for all x?
A) f(x) = 1-x
B) f(x) =1 - (x^2)
C) f(x) = x^2 - (1-x)^2
D) f(x) = x^2 * (1-x)^2
E) f(x) = x/(1-x)
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Re: f(x) mess [#permalink] New post 18 Aug 2008, 13:02
brokerbevo wrote:
For which of the following functions f is f(x) = f(1-x) for all x?
A) f(x) = 1-x
B) f(x) =1 - (x^2)
C) f(x) = x^2 - (1-x)^2
D) f(x) = x^2 * (1-x)^2
E) f(x) = x/(1-x)


D
f(x) = x^2 * (1-x)^2
f(1-x)= (1-x)^2 * (1-(1-x))^2)=(1-x)^2 * x^2=f(x)
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Re: f(x) mess [#permalink] New post 18 Aug 2008, 13:17
x2suresh wrote:
brokerbevo wrote:
For which of the following functions f is f(x) = f(1-x) for all x?
A) f(x) = 1-x
B) f(x) =1 - (x^2)
C) f(x) = x^2 - (1-x)^2
D) f(x) = x^2 * (1-x)^2
E) f(x) = x/(1-x)


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


But if x = 3 (for example)-->
    f(x) ---> f(3) = 3^2 * (1-3)^2 ---> 9 * 4 = 36
    f(1-x) ---> f(1-3) = -2^2 * (-2-3)^2 ---> 4 * 25 = 100

It does not work b/c 36 does not equal 100. Could someone please explain.
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Re: f(x) mess [#permalink] New post 18 Aug 2008, 13:29
brokerbevo wrote:
x2suresh wrote:
brokerbevo wrote:
For which of the following functions f is f(x) = f(1-x) for all x?
A) f(x) = 1-x
B) f(x) =1 - (x^2)
C) f(x) = x^2 - (1-x)^2
D) f(x) = x^2 * (1-x)^2
E) f(x) = x/(1-x)


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


But if x = 3 (for example)-->
    f(x) ---> f(3) = 3^2 * (1-3)^2 ---> 9 * 4 = 36
    f(1-x) ---> f(1-3) = -2^2 * (-2-3)^2 ---> 4 * 25 = 100

It does not work b/c 36 does not equal 100. Could someone please explain.


Please check the highlighted part.. you are doing wrong.

f(1-x) ---> f(1-3) =f(-2) = -2^2 * (1-(-2))^2 ---> 4 * (-3)^2 = 36
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Manager
Manager
User avatar
Joined: 11 Apr 2008
Posts: 129
Location: Chicago
Followers: 1

Kudos [?]: 33 [0], given: 0

Re: f(x) mess [#permalink] New post 18 Aug 2008, 13:52
x2suresh wrote:
brokerbevo wrote:
x2suresh wrote:

But if x = 3 (for example)-->
    f(x) ---> f(3) = 3^2 * (1-3)^2 ---> 9 * 4 = 36
    f(1-x) ---> f(1-3) = -2^2 * (-2-3)^2 ---> 4 * 25 = 100

It does not work b/c 36 does not equal 100. Could someone please explain.


Please check the highlighted part.. you are doing wrong.

f(1-x) ---> f(1-3) =f(-2) = -2^2 * (1-(-2))^2 ---> 4 * (-3)^2 = 36


Woops. :shock: Thanks for that catch.
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Factorials were someone's attempt to make math look exciting!!!

Re: f(x) mess   [#permalink] 18 Aug 2008, 13:52
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