Given x^{2}g(x) + g(1-x) = 2x-x^{4}, the problem is to find g(0). What I did was I evaluated the equation using 0. It therefore becomes:

(0)g(0) + g(1-0) = 0

g(1) = 0

Then, I evaluated the equation with 1 so it becomes:

1g(1) + g(1-1) = 2-1

g(1) + g(0) = 1

Since g(1) = 0, then:

g(0) = 1.

I'm not really sure if what I did was right, because the solution seems too simple. I would like to ask for clarification if what I did was right.

Thanks in advance.