There is not one set investment demand function in the sense that there is one Pythagorean theorem or one equation for the money multiplier. Instead, the investment demand function is something that can change. It is simply the relationship between the interest rate and the amount of investment that is demanded.
This curve can shift for a variety of reasons, and that means that the function can change when those factors change. In other words, we know that there is a relationship between the interest rate and the amount of investment, but we do not know exactly what that relationship is, because it varies as other factors vary.