The title might be misleading but I have forgotten how these functions are called. I am referring to cases such as:
$$7sin(y) + 0.9cos(y/4) = x_1sin(y) + x_2cos(y/4)$$
where we know that $x_1 = 7$ and $x_2 = 0.9$.
Another example would be polynomials:
$$5y^2 + 4y -12 = x_1y^2 + x_2y -x_3$$
where again the $x_i$ can be trivially found by equating the same-power terms.
Q: Generally speaking what conditions should, say $f(y)$ & $g(y)$ satisfy so that $x_1f(y) + x_2g(y) = 0$ requires $x_1 = 0$ and $x_2 = 0$?