# Thread: Problem on basic functions clarification

1. ## 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.

2. ## Re: Problem on basic functions clarification

Looks good to me.

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

3. ## Re: Problem on basic functions clarification

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

$g(x)=-x^2+1 \Rightarrow g(0)=1 \,\,\, g(1)=0$

Now If your calculation is correct that should satisfy the equation you gave

$x^2g(x)+g(1-x)=2x-x^4$

$x^2(1-x^2)+(1-(1-x)^2)=2x-x^4$

$x^2-x^4+1-x^2+2x-1=2x-x^4$

$0=0 \,\,$ so your calculation is correct ...

4. ## Re: Problem on basic functions clarification

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