for which of the following function f is F(x)=f(1-x) for all x
f(x)=1-x
f(x)=1-x^2
f(x)=x^2-(1-x)^2
f(x)=x^2(1-x)^2
f(x)=x/1-x
f(x)=1-x
f(x)=1-x^2
f(x)=x^2-(1-x)^2
f(x)=x^2(1-x)^2
f(x)=x/1-x
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Source: Beat The GMAT — Problem Solving |
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Anurag@Gurome
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Refer to the post here >> https://www.beatthegmat.com/gmat-functio ... tml#411296
Anurag Mairal, Ph.D., MBA
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Brent@GMATPrepNow
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Let's try plugging in an easy value for x. How about x = 0.B166418 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
So, we can reword the question as, For which of the following functions is f(0)=f(1-0)
In other words, we're looking for a function such that f(0) = f(1)
A) f(x)=1-x
f(0)=1-0 = 1
f(1)=1-1 = 0
Since f(0) doesn't equal f(1), eliminate A
B) f(x) = 1 - x^2
f(0) = 1 - 0^2 = 1
f(1) = 1 - 1^2 = 0
Since f(0) doesn't equal f(1), eliminate B
C) f(x) = x^2 - (1-x)^2
f(0) = 0^2 - (1-0)^2 = -1
f(1) = 1^2 - (1-1)^2 = 1
Since f(0) doesn't equal f(1), eliminate C
D) f(x) = x^2(1-x)^2
f(0) = 0^2(1-0)^2 = 0
f(1) = 1^2(1-1)^2 = 0
Since f(0) equals f(1), keep D for now
E) f(x) = x/(1-x)
f(0) = 0/(1-0) = 0
f(1) = 1/(1-1) = undefined
Since f(0) doesn't equal f(1), eliminate E
Since only D satisfies the condition that f(x)=f(1-x) when x=0, the correct answer is D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
yeah even i thought by doing this way but it took much time ....
was wondering if some other way of doing this
was wondering if some other way of doing this
GMAT/MBA Expert
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Brent@GMATPrepNow
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You can also analyze each function algebraically (as Anurag does here: https://www.beatthegmat.com/gmat-functio ... tml#411296), but that approach also takes time.B166418 wrote:yeah even i thought by doing this way but it took much time ....
was wondering if some other way of doing this
It comes down to what you feel more comfortable with: plugging in numbers vs. algebraic manipulation
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
