Question

If 2 f left parenthesis x right parenthesis plus f left parenthesis 1 minus x right parenthesis equals x squared2f(x)+f(1 − x)=x2 what is f​(x​)?

Answer 1

If you would like to know what is f(x), you can find this using the following steps:

f(x) = ?
2 * f(x) + f(1-x) = x^2
2 * f(x) = x^2 - f(1-x)       /2
f(x) = (x^2 - f(1-x)) / 2
f(x) = x^2 / 2 - f(1-x) / 2

The correct result would be f(x) = x^2 / 2 - f(1-x) / 2.