f(x) = f(1-x)
f(x) = 1-x
substitution x with 1-x we get f(1-1+x) = f(x)
Is the first choice the right answer?..

Answer should be D


I hate these type of questions as they are very new to me. But what I did was substitue x with 1-x and the answer should be the same for the equation if u use x or 1-x

ri2007 wrote:Answer should be D


I hate these type of questions as they are very new to me. But what I did was substitue x with 1-x and the answer should be the same for the equation if u use x or 1-x

can you work it out and show it to us.. still dont get how D is the answer

I think A shud be the Ans...

Given,
f(x) = f(1-x)

for x = 3, f(1-x) = -2
and for x = -2, f(1-x) = 3,

The only option that satisfies this is A.

You are given different equations for f(x). Since you know that f(x) = f(1-x) when you substitute the x with (1-x) the answer should be the same.

Now ans choice D is f(x) = x^2 (1-x)^2

So just substitute x with (1-x) you get

f(1-x) = (1-x)^2 (1-(1-x))^2

= (1-x)^2 (x)^2

So f(x) = x^2 (1-x)^2 = f(1-x)

hey thnks for d explanation..yeah the OA is D..not A..

manasi_sh wrote:hey thnks for d explanation..yeah the OA is D..not A..

What does the statement below actually mean
For which of the following functions f is f(x)=f(1-x),

doesnt it mean that i should get a function f, where f(x) = f(1-x), so if substituting 1-x in the place of x should give f(x), then isnt A the option.

Can someone give some insight as to how to handle questions dealing with functions and what are the type of questions one can expect related to functions?

phawa any tips will be great.

I got this problem wrong again while I took the test..
Thought Ill repost, then decided to update this old post.
Can anyone comment how functions related problems are to be addressed.

In the above case as pointed by Suyog, why not A as the answer?

gmatrant wrote:I got this problem wrong again while I took the test..
Thought Ill repost, then decided to update this old post.
Can anyone comment how functions related problems are to be addressed.

In the above case as pointed by Suyog, why not A as the answer?

I tend to just plug in numbers to the given function to see what its really saying, rather than interpreting the sometimes cryptic function statements.

So for this question you plug in 1 (randomly chosen, but a good starting point) for x then we get f(1)=f(1-1)=f(0). So it's saying f(1) must equal f(0).

So now you goto the answers and plug in 1 and 0 to see if one equation yields the same answer.

So when you plug in 1 into function A, [f(x)=1-x] f(1)=1-1=0
and from above you know that f(1) must equal f(0), so now try 0 in the equation. f(0)=1-0=1 So 1 /= 0 so A doesn't work.

Now onto D, [f(x)=x^2(1-x)^2] f(1)=0 and f(0)=0. This works but I would try two other numbers just to be sure. So f(2) and f(1-2)=f(-1).
f(2)=4 and f(-1)=4 so D does work.

you dont have to pick numbers.....lets take the first one f(x)=1-x that means f(1-x)=1-(1-x) thus f(1-x)=x which is not equal to f(x). substitute and to the other equations and you will find the solution

I think the answer is D to this question. Here is the explanation

Question ask for which of the function does f(x) = f(1-x) is true for all x

Now try each answer choice.

Fortunately I tried first with D

D Choice is f(x) = x^2(1-x)^2 - Lets make this eqn 1

Try writing the above function in terms of f(1-x)
f(1-x) = (1-x)^2[1-(1-x)]^2 (I have replaced x with 1-x in eqn 1)
f(1-x) = (1-x)^2x^2 as 1 will get cancel
The above value is the same as f(x).

Thanks.

-A

i got lost on the "for all values x" phrase. I love to test numbers and plug in and backsolve. Yes its time consuming but its cold hard evidence for the right answer. for this questioncant we just plug in 1 and get an answer then 0 and get the same answer.Is the question answer choice that gives the same answer for each number the correct choice? Choice D?

please correct my logic if I am wrong!

Enginpasa1 wrote:i got lost on the "for all values x" phrase. I love to test numbers and plug in and backsolve. Yes its time consuming but its cold hard evidence for the right answer. for this questioncant we just plug in 1 and get an answer then 0 and get the same answer.Is the question answer choice that gives the same answer for each number the correct choice? Choice D?

please correct my logic if I am wrong!

You can definately just plug in numbers for this question. To each his own, some people like to plug in real numbers (like 1=x, therefore 1-x=0 as you did) while others like to work with the variables (plugging in 1-x wherever they see x in the equation). If done correctly, both methods will work out to give you the same answer = D

thought id revisit this post. i came across it on my practice test and got it wrong. after looking at the explanations in this post and given the little that i know about functions, here is how i intepreted the question and please correct me if i am wrong as i am still confused

1) translation of the question
FOR WHICH OF THE FOLLOWING FUNCTIONS f is f(x) = f(1-x) FOR ALL x?
in other words, for all functions of x anywhere you see x and replace it with 1-x, will produce an answer that is equal to its function? or better, out of the listed functions, which function will equal its output?

if that's a correct way of rewording the question please let me know.