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parulmahajan89: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri May 11, 2012 9:06 pm

GMAT prep -Question

by parulmahajan89 » Sun Sep 01, 2013 8:53 am

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

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Source: Beat The GMAT — Problem Solving | Sun Sep 01, 2013 8:53 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 01, 2013 9:01 am

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