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 .
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 .