For which of the following functions f is f (x) = f (1 – x) for all x ?

Question

For which of the following functions f is f(x) = f(1-x) for all x?  
    
A. f(x)=1−xf(x)=1−x  
    
B. f(x)=1−x2f(x)=1−x2  
    
C. f(x)=x2−(1−x)2f(x)=x2−(1−x)2  
    
D. f(x)=x2∗(1−x)2f(x)=x2∗(1−x)2  
    
E. f(x)=x(1−x)  
    
Can anyone please help me out on this one? #GMAT #gmatprep

Ashlesha Kanoje · Answer

A.
1−x?1−(1−x)1−x?1−(1−x)
1−x?1−1+x1−x?1−1+x
1−x?x1−x?xNOT EQUAL!

B.
1−x2?1−(1−x)21−x2?1−(1−x)2
1−x2?2x+x21−x2?2x+x2 NOT EQUAL!

C.
x2−(1−x)2?(1−x)2−(1−(1−x))2x2−(1−x)2?(1−x)2−(1−(1−x))2
x2−(1−x)2?(1−x)2−x2x2−(1−x)2?(1−x)2−x2 NOT EQUAL!

D.
x2(1−x)2?(1−x)2(1−(1−x))2x2(1−x)2?(1−x)2(1−(1−x))2
x2(1−x)2?(1−x)2(x)2x2(1−x)2?(1−x)2(x)2 EQUAL!

Answer: D

Jaideep Hooda · Answer

Ah, thanks hn!

No Dox · Answer

I mean you could factor out f(x) 's in every equation, but from choices, option E is obviously correct, as x -> 1-x and 1-x -> 1-(1-x)

If it's a single answer correct type question, probably not worth solving equations in A-D in the interest of time

For which of the following functions f is f (x) = f (1 – x) for all x ?

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