Thread: Problem on basic functions clarification

Given x²g(x) + g(1-x) = 2x-x⁴, 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.

Looks good to me.

If it seems too easy why not try to find out more about the function?

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 ...

Thanks for your help. At least I know I'm on the right track.