If g(x) satisfies 4g(x) + g(1-x) = 3x^{2}, what is what is g(x)?

I'm really stuck, what is a possible solution?

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- August 24th 2012, 04:16 PMernestjohnFinding the function that will satisfy the equation.
If g(x) satisfies 4g(x) + g(1-x) = 3x

^{2}, what is what is g(x)?

I'm really stuck, what is a possible solution? - August 24th 2012, 05:13 PMProve ItRe: Finding the function that will satisfy the equation.
I expect since this particular combination of functions gives you a quadratic, you will probably find that g(x) is a quadratic. So let , then . So

So this means .

Therefore a function which satisfies your original equation is . - August 24th 2012, 05:52 PMMaxJasperRe: Finding the function that will satisfy the equation.
Simple solution:

Substitute ...you get a second equation, eliminate g(1-x) between them to obtain g(x):

- August 24th 2012, 09:55 PMrichard1234Re: Finding the function that will satisfy the equation.
Replace with to obtain

. We already know

Multiply the second equation by -4 and add them.

Divide both sides by -15 and simplify.