An algebra problem by Arie Nugroho

Algebra Level 2

Given that the equation f(x) + xf(1-x) = x holds for every real number x. The value of f(-1) + f(1) is

source : SIMAK UI

-1 4/3 1/3 1

2 solutions

Patrick Corn
Oct 13, 2014

It shouldn't be hard to prove that $f(x) = \frac{x^2}{x^2-x+1}$ . Details left to the reader.

Mr. Corn, can you please explain the solution. I have no idea, how to arrive at the function with the given condition of f(x).

Arun Jp - 6 years, 8 months ago

Arun Jp
Oct 13, 2014

given, f(x) + xf(1-x) = x. for x = 2, f(2) + 2f(-1) = 2.
for x = -1, f(-1) - f(2) = -1.
which gives, f(-1) = 1/3 0n elimination of f(2).
and for x = 1, f(1) + f(0) = 1.
for x = 0, f(0) + 0 = 0.
which gives f(1) = 1.
so, f(-1) + f(1) = 1/3 + 1 = 4/3...

An algebra problem by Arie Nugroho

2 solutions

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