For which of the following functions does f(x) = f(2 - x) ?

Question

For which of the following functions does  f(x)=f(2-x) ?

A.  f(x)=x+2

B.  f(x)=2x-x^2

C.  f(x)=2-x

D.  f(x)=(2-x)^2

E.  f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4? 
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1

blueseas · Accepted Answer

hi,

in all the option just put 2-x in place of x

A. f(x)=x+2===>f(2-x)=2-x+2=4-x==>not equal

B. (fx)=2x-x^2====>f(2-x)=2(2-x)-(2-x)^2=4-2x-x^2+4x-4=2x-x^2===>equal==correct

C. f(x)=2-x===>f(2-x)=2-(2-x)=x===>not equal

D. f(x)=(2-x)^2===>f(2-x)=(2-2+x)^2=x^2===>not equal

E. f(x)=x^2===>f(2-x)=(2-x)^2===>not equal

hence only B satisfies.

dont plug in this

hope it helps.

Bunuel · Answer

If you plug x=1 then all options will work, since f(x)=f(1) and f(2-x)=f(1) too. For such kind of questions it's not a good idea to plug 0, -1 or 1. Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. Similar questions: functions-problem-need-help-93184.html for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html let-the-function-g-a-b-f-a-f-b-143311.html for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html Hope it helps.

Vinayprajapati · Answer

If we plug x=0 then, f(0)=f(2)
A. F(0)= 2 and f(2)= 4
B. f(0)= 0 and f(2)= 0
C. F(0)= 2 and f(2)= 0
D. F(0)= 4 and f(2)= 0
E. f(0)= 0 and f(2)= 4

Hence b is the correct answer.

veergmat · Answer

It can be easily done in less than a minute simply by elimination or substitution method.

1) f(x)=x+2; for x=2-x , f(2-x)=4. Eliminated
 2) f(x) = 2x-x^2; for x=2-x ,f(2-x)=2(2-x)-(2-x)^2 =(2-x)(2-2+x)=2x-x^2 
3) f(x) = 2 - x; for x=2-x, f(2-x)=x . Eliminated
4) f(x)=(2-x)^2; for x=2-x, f(2-x)=(x)^2 . Eliminated
5) f(x)=x^2;for x=2-x, f(2-x)=(2-x)^2. Eliminated

Nunuboy1994 · Answer

What confuses my about this question, with answer "B," is an example in which you have f(2-3)

f(2-3)=-1

F(x)= 2(2-x)-(2-x)^2
F(2-3)= 2(2-3)-(2-3)^2
F(2-3)= 2(-1)-(-1)^2
F(2-3)= -2-1
F(2-3)= -3?

Maybe I'm tired or something but I keep coming to this conclusion.

SamBoyle · Answer

A good way to solve it is like this. Essentially the question is saying F(X) so everytime you see an X you're going to sub in the function 2-x. A good video explaining how functions work is here since most people here do a crappy job. https://www.youtube.com/watch?v=T6-Zdr5w_bE

testcracker · Answer

hi

let f(0) = f(2)

B: f(0) = 0
f(2) = 4 - 4 = 0

so f(0)= f(2)
B is the answer

thanks

KanishkM · Answer

A. f(x)=x+2
f(2-x) = 2-x+2, Not equal

B. f(x)=2x-x^2
f(2-x) = 2*(2-x) - (2-x)^2 = 4-2x-   = 2x-x^2

C. f(x)=2-x
f(2-x) = 2-2+x = x, Not equal

D. f(x)=(2-x)^2
f(2-x)= (2-2-x)^2 , Not equal

E. f(x)=x^2
f(2-x) = (2-x)^2, Not equal

Answer B

Adit_ · Answer

Take a number like x=0, then f(0)=f(2)

Substitute x=0 and x=2 for all the options and they must be equal.
Only  option B  does that.

___________________

Substituting 1 would give f(1)=f(1) ur comparing two values that will be the same definitely. Hence one must not use 1 here.

egmat · Answer

Hi Nunuboy1994,

Your calculation of f( 2 - 3 ) = f( -1 ) =  -3  is actually perfectly correct! The issue is you stopped halfway — you only computed one side of the equation.

The property f(x) = f( 2 -x) means: for any x you pick, f(x) and f( 2 -x) should give the same result.

Let's pick x = 3 and check BOTH sides:

Left side:  f(x) = f( 3 )
f( 3 ) =  2 ( 3 ) - ( 3 )2 =  6  -  9  =  -3

Right side:  f( 2 -x) = f( 2 - 3 ) = f( -1 )
f( -1 ) =  2 ( -1 ) - ( -1 )2 =  -2  -  1  =  -3

Both sides equal  -3 . It works!

You correctly got f( -1 ) =  -3  but  never compared it against f( 3 ) . Once you compute f( 3 ) =  -3  as well, you can see they match perfectly.

Try another pair to build confidence.  Let x =  0 , so  2 -x =  2 :

f( 0 ) =  2 ( 0 ) - ( 0 )2 =  0 
f( 2 ) =  2 ( 2 ) - ( 2 )2 =  4  -  4  =  0

Again, both equal  0 .   Key Insight:  The function is symmetric around x =  1 , which is exactly what f(x) = f( 2 -x) means — the graph is a mirror image on either side of the line x =  1 .

Answer: B

For which of the following functions does f(x) = f(2 - x) ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

For which of the following functions does f(x) = f(2 - x) ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards