for which function f is f(x) = f(1- x) for all? a. f(x) =

Question

for which function f is f(x) = f(1- x)  for all?

a. f(x) = 1-x
b. f(x) = 1- x^2
c. f(x) = x^2 - (1-x)^2
d. f(x) = x^2(1-x)^2
e. f(x) = x/(1-x)

Please explain answer. thx!

chriswil2005 · Answer

Is there an error in the stem? I am not sure what you mewan by f(1-1), does that mean f(0)? I think you meant to write f(x)=f(1-x), correct?

If so, then my answer is D. Pick a number for x (I chose 5) and plug it to see if any answers has that are equal for x (in my case, the number 5) and 1-x (in my case, -4).

Also, the stem could have bee f(x)=f(x-1) and D still would have been the answer.
Let me know if there is an error. thanks

laxieqv · Answer

I guess there's error posting the question,too.

olorin · Answer

If Chris is right about the question being f(x) = f(1-x) then D would be my answer.

Jennif102 · Answer

Yeah, there was a typo in my question stem- it's supposed to be 1-x
sorry!
D is correct. 
THanks for the explanation - this is one of those fairly simple questions that you just need a refresher on. thanks a lot!

rahulraao · Answer

Hey Chris, Im really lost when it comes to plugging the number into the functions. Would you mind actually working it out? Thanks!!

chriswil2005 · Answer

Sure. I use x=5, so 1-x=-4. Since f(x)=f(1-x), we are looking for an equation that creates answer that are equal when x=5 and x=-4. I usually set up a table sorta like this:
x , 1-x
5 , -4
-----------------------------------------------------------------------
A. -4 , 5
B. -24, -15
C. 9, -9
D. (25)(16), (16)(25)
E. -5/4, -4/5

As you can see, choice D has the same value for x and 1-x. I hope this is clear, if not let me know where I need to emphasize.

Note: I know the table is not clear as the formatting cannot be perfected

GMATT73 · Answer

I am still totally lost :?:

Where are the comma in the answer choices??

chriswil2005 · Answer

yea, bad table. here is an excel format. It is lots clearer. Again, let me know of any problems.

sudhagar · Answer

chriswil2005: Do you use any strategy in picking numbers?

I simply go with random choices. This might consume lot of time on exam. If there is any strategy, then that would help us in saving time.

rahulraao · Answer

AWESOME! Chris, thanks a ton buddy!

chriswil2005 · Answer

My strategy for picking numbers requires 2 stipulations:
1. I have to make sure the question is apt to picking numbers. That is, I have to make sure that picking numbers will work. For this question, you know that involves a function of x. There are no restrictions, such as x is a positive integer or a prime greater than 10. Therefore f(x)=f(1-x) for any real number x, so picking any real number in this case will work. As you all know I picked 5.

2. When you determine that a question is good for picking numbers, pick a good easy number to work with. In most cases, I WILL NOT pick 1 or 2. The test writers know about the picking numbers method and put traps in the questions that several answers will work for 1 or 2, but not all numbers. That is why I picked 5. 10 in a good number in most cases. 

Overall, I think it is a good strategy and a question like this takes me about a minute to 1.5 minutes.

Anything else, let me know. I hope this helps

HongHu · Answer

You would be able to pick D by just eyeballing the choices. For all the other options there isn't a symetry for x and (1-x), but for D if you substitue x by (1-x) you get exactly the same thing. This is how you are supposed to approach this kind of problems. That is, to substitute all x with (1-x) for all functions. Picking numbers should be used as a double check.

sudhagar · Answer

Thanks Chris. Your explanation helps. Most of the times I used to pick up 1 & 2, as it would be easier to compute. 

I would practice picking up other numbers. Also for this question, Hong's comment was a quicket shortcut. We would be able to nail down the choice and apply some numbers to confirm it.

for which function f is f(x) = f(1- x) for all? a. f(x) =

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