ZOMGSH! Math Question?

Question

If 2f(x)+f(1-x)=x^2 for all x, then f(x)=?

Answer 1

Clearly, f(x) is at least quadratic. So, set it up with variable coefficients:

f(x) = ax^2 + bx + c

The plug in:

2(ax^2 + bx + c) + a(1 - x)^2 + b(1 - x) + c = x^2

Multiply it out and collect similar terms, then correlate coefficients. The coefficient of the quadratic term will have to be 1 and the coefficient of the linear and constant terms will have to be 0. You'll have three equations in three unknowns, so you can find a, b and c. (It turns out to be pretty easy to do.)

Answer 2

Well, this is the blind leading the blind. Forty years ago, you usually did not even see algebra until H.S., and I did not qualify for Alg, II, so I feel your pain.

I would rewrite the equation

fx + fx + 1 - fx = xx

Simplify that to fx + 1 = xx. Then divide both sides by x., so f +1 = x. Then multiply both sides by f. So f^2 + f = fx. Does that seem right?

LOL I hope a math person jumps in,,,