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Algebra Level 3

For which of the following functions of f ( x ) f(x) satisfy the equation f ( x ) = f ( 1 − x ) f(x) = f(1-x) \; ?

f ( x ) = 1 − x f(x) = 1-x f ( x ) = x 1 − x f(x) = \frac{x}{1-x} f ( x ) = x 2 − ( 1 − x ) 2 f(x) = x^2-(1-x)^2 f ( x ) = 1 − x 2 f(x) = 1-x^2 f ( x ) = x 2 ( 1 − x ) 2 f(x) = x^2(1-x)^2

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Manav D.S.R by Manav D.S.R , 19, Thailand

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2 solutions

Manav D.S.R
Mar 24, 2016

Solution to this problem is:

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

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Shivam Mishra
Mar 26, 2016

It is pretty easy to observe that f ( 0 ) = f ( 1 ) f(0)=f(1) by putting x = 0 x=0 .Now going through the options reveals that only the fourth option satisfies our obtained condition.Hence the required answer is f ( x ) = x 2 ( 1 − x ) 2 f(x)=x^2(1-x)^2

1 Helpful 1 Interesting 0 Brilliant 0 Confused

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