parulmahajan89 wrote:For which of the following functions F is F(X)=f(1-x) for all x?
F(x)= 1-x
F(X)=1-x2
F(X)=x2-(1-x2)
F(X)=x2(1-x2)
F(X)=X/1-X
Not sure which method to take. Do I plug in different values for X? It would take time right?
Please help for right answer and right approach. Thanks
Plugging in a value for x won't take much time, as long as you use a "nice" value for x.
How about x =
0?
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
