Looks good to me.
If it seems too easy why not try to find out more about the function?
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.
If you see the points of g(x) you can easily derive the functions so it has the points (0,1)..(1,0)
This can be interpreted as a parabola
Now If your calculation is correct that should satisfy the equation you gave
so your calculation is correct ...