f(x)=f(1-x)?
a) f(1-x) = 1- (1-x) = x != f(x) incorrect
b) f(1-x) = 1 - (1-x)^2 = 1 - (1+x^2 - 2x) = 2x - x^2 !=f(x) incorrect
c) f(1-x) = (1-x)^2 - (1-(1-x))^2 = (1-x)^2 - x^2 = -f(x) incorrect
d) f(1-x) = (1-x)^2 *(1-(1-x))^2 = (1-x)^2 * (x)^2 = f(X) correct
e) f(1-x) = (1-x)/x = 1/f(x) incorrect
IMO D
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Cans!!
Substitute x = 1-x in all the answer choices.
For f(x) = f(1-x) ; both should be equal
Only in D it is equal.
For f(x) = f(1-x) ; both should be equal
Only in D it is equal.
myfish wrote:Thank you so much for showing me how to do this one.
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Plug x = 1 - x in the options.myfish wrote:Thank you so much for showing me how to do this one.
(A) f(x) = 1 - x, f(1 - x) should give the same value i.e. 1 - x when x = 1 - x
f(1 - x) = 1 - (1 - x) = 1 - 1 + x = x. Not True.
(B) f(x) = 1 - x², f(1 - x) = 1 - (1 - x)². Not True.
(C) f(1 - x) = (1 - x)² - [1 - (1 - x)²]. Not True.
(D) f(x) = x²(1 - x)²; f(1 - x) = (1 - x)² [1 - (1 - x)]² = (1 - x)²[1 - 1 + x]² = (1 - x)²(x)² = f(x). True.
The correct answer is D.
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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.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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