Function f(x) problem
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GMATGuruNY
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Let x=2.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-x²
c. f(x)= x²-(1-x)²
d. f(x)= x²(1-x)²
e. f(x)= x/(1-x)
Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1).
The question becomes:
For which of the following functions does f(2) = f(-1)?
Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.
Answer choice B:
f(2) = 1 - 2² = -3.
f(-1) = 1 - (-1)² = 0.
Doesn't work.
Answer choice C:
f(2) = 2² - (1-2)² = 4 - 1 = 3.
f(-1) = (-1)² - [1-(-1)]² = 1-4 = -3.
Doesn't work.
Answer choice D:
f(2) = 2² * (1-2)² = 4 * 1 = 4.
f(-1) = (-1)² * [1-(-1)]² = 1 * 4 = 4.
Success!
Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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Brent@GMATPrepNow
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Mitch's solution is perfect. Here's another version where we test the values using x = 0For which of the following functions f is f(x)=f(1-x) for all x?
A) f(x) = 1-x
B) f(x) = 1-x²
C) f(x) = x² - (1-x)²
D) f(x) = x²(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 - x²
f(0) = 1 - 0² = 1
f(1) = 1 - 1² = 0
Since f(0) doesn't equal f(1), eliminate B
C) f(x) = x² - (1-x)²
f(0) = 0² - (1-0)² = -1
f(1) = 1² - (1-1)² = 1
Since f(0) doesn't equal f(1), eliminate C
D) f(x) = x²(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
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Brent@GMATPrepNow
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Here's a similar question to practice with:
https://www.beatthegmat.com/number-systems-t270738.html
Cheers,
Brent
https://www.beatthegmat.com/number-systems-t270738.html
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
