1. ## Limits #1

Given a function $f$ of a real variable which satisfies the function defined by $f (x) + x \times f(1-x) = 1 +x^2$, for all real $x$, determine $f(x)$.

Please explain to me what to do. Ive never done calculus before and this is the question I was given.

2. $f(x)+xf(1-x)=1+x^2$

Replace $x$ with $1-x$:

$f(1-x)+(1-x)f(x)=1+(1-x)^2\Rightarrow f(1-x)=x^2-2x+2-(1-x)f(x)$

Now replace $f(1-x)$ in the first equality and find $f(x)$.