In place of X you simply substitute (1-X) and see for which of the functions you get the same value that you started off with.
A must do question since the choice doesnt have "None of these" thereby letting you know that one of the options must be the correct answer.
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Simple one...still pls explain
Source: Beat The GMAT — Problem Solving |
I'm having a hard time with these problems... can you please show me an example? THANKS!Neo2000 wrote:In place of X you simply substitute (1-X) and see for which of the functions you get the same value that you started off with.
A must do question since the choice doesnt have "None of these" thereby letting you know that one of the options must be the correct answer.
First, you have to understand what f(1-x) does. As Neo2000 stated, it means every time you see an 'x', substitute it with '(1-x)'.
For example,
f(x) = 1-x
Then
f(1-x) = 1-(1-x) = 1-1+x = x
For this problem, you need find the solution where f(x) and f(1-x) are the same. If you test each answer choice, you will see that D matches that criteria.
f(x) = x^2 * (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
x^2 * (1-x)^2
which is f(x)
For example,
f(x) = 1-x
Then
f(1-x) = 1-(1-x) = 1-1+x = x
For this problem, you need find the solution where f(x) and f(1-x) are the same. If you test each answer choice, you will see that D matches that criteria.
f(x) = x^2 * (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
x^2 * (1-x)^2
which is f(x)
I FINALLY GET IT! Thank YOU!tmmyc wrote:First, you have to understand what f(1-x) does. As Neo2000 stated, it means every time you see an 'x', substitute it with '(1-x)'.
For example,
f(x) = 1-x
Then
f(1-x) = 1-(1-x) = 1-1+x = x
For this problem, you need find the solution where f(x) and f(1-x) are the same. If you test each answer choice, you will see that D matches that criteria.
f(x) = x^2 * (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
x^2 * (1-x)^2
which is f(x)
